Q&A Hero

Q: The manager of a branch bank wants to build a simulation model of the lobby operation to reduce the waiting time of her customers. The number of tellers is an example of: A) a decision variable. B) an uncontrollable variable. C) a time-compressed variable. D) a dependent variable.

Q: Which one of the following relationships is correct? A) Decision variables reflect the value of uncontrollable variables. B) Dependent variables reflect the value of decision and uncontrollable variables. C) Uncontrollable variables reflect the value of decision variables. D) Uncontrollable variables reflect the values of dependent variables.

Q: A manager has been given the table shown below and is asked to generate random numbers. Which of the following statements is true? Range # Customers 00-49 0 50-79 1 80-99 2 A) There are no customers in the store 49 percent of the time. B) The probability of having one customer in the store is 0.30. C) The relative frequency of having two customers in the store is 0.80. D) If we randomly choose the numbers 0 through 99 enough times, about 99 percent of the time we will have two customers in the store.

Q: Random variables are under the control of the decision maker.

Q: Any random number has the same likelihood of being selected as any other, regardless of how recently it has been selected.

Q: Monte Carlo simulation is the use of computer graphics to show customers or products moving through a series of process steps.

Q: What are the differences between decision variables and uncontrolled variables? Describe the differences and provide an example from a simulation model.

Q: What are the motivations for using simulation for analyzing processes?

Q: What is meant by time compression in a simulation model?

Q: What is the difference between a waiting line model as described in Supplement B and a simulation model of a waiting line problem?

Q: ________ is a feature of simulation models that allows them to obtain operating-characteristic estimates in much less time than is required to gather the same operating data from a real system.

Q: ________ is the act of reproducing the behavior of a system using a model that describes the processes of the system.

Q: Using a simulation model to gather a year of operating data in a few minutes is known as: A) historical search data collection. B) Monte Carlo optimization. C) sub-optimization. D) time compression.

Q: Simulation models are: A) useful when waiting line models are too complex. B) useful for conducting experiments using the real system. C) preferred because they find optimal solutions. D) usually inexpensive relative to other approaches.

Q: A simulation model: A) describes operating characteristics with known equations. B) replicates the service of customers and keeps track of characteristics such as the number in line, the waiting time, and the total time in the system. C) prescribes what should be done in a situation. D) finds the optimal solution to a problem without having to try each alternative.

Q: Time compression is the feature of simulation that allows managers to obtain operating-characteristic estimates in much less time than is required to gather the same operating data from a real system.

Q: Simulation is the process of reproducing the behavior of a system using a model that describes the processes of the system.

Q: A snack food producer runs four different plants that supply product to four different regional distribution centers. The division operations manager is focused on one product, so he creates a table showing each plant's monthly capacity and each distribution center's monthly demand (both amounts in cases) for the product. The division manager supplements this table with the cost data to ship one case from each plant to each distribution center. Formulate an objective function and constraints that will solve this problem using linear programming. Center 1 Center 2 Center 3 Center 4 Monthly Capacity Plant A $2 $7 $5 $4 8,000 Plant B $9 $4 $7 $6 12,000 Plant C $7 $6 $4 $3 7,500 Plant D $4 $8 $3 $5 5,000 Monthly Demand 9,000 8,500 8,000 7,000

Q: Provide three examples of operations management decision problems for which linear programming can be useful, and why.

Q: Table D.3 The Harper Company is in the process of production planning for the next four quarters. The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand. Anticipation inventory is also allowed, but not backorders. Undertime is paid, at a rate of $5.00 per unit. The beginning (or current) inventory is 25 units. Details are shown in the following POM for Windows table. Use the information in Table D.3. Given the information in the optimal tableau, what is the subcontracting cost, in dollars per unit? A) $5 B) $7 C) $10 D) $12

Q: Table D.2 Bahouth Enterprises produces a variety of hookahs for clients around the globe. Their small plant has a highly flexible workforce that can switch between products seamlessly. They forecast using a six-month planning period and have a demand forecast as shown in the table. The per-unit costs for each output option the sales and operations planner has at his disposal are indicated in the table. Regular output costs $40 per unit, overtime production is $60 per unit, and subcontracting is $70 per unit. Holding inventory from one month to the next costs $2 per unit per month and a backlog costs $5 per unit per month. Regular plant capacity is 300 units per month. Period 1 2 3 4 5 6 Total Forecast 400 350 500 400 500 200 2,350 Output Regular $40 1,800 Overtime $60 0 Subcontract $70 0 Inventory Beginning 0 Ending $2 Average 0 Backlog $5 2,250 Costs Use the information in Table D.2. The plant has no limits on the number of units produced by overtime or subcontractors and adopts a level plan strategy for the six-month planning period. What is the cost for month 6 of their level plan? A) between $16,200 and $16,600 B) between $16,600 and $17,000 C) between $17,000 and $17,400 D) between $17,400 and $17,800

Q: Use the information in Table D.2. If the planner decides to adopt a chase plan for the planning period, what will the regular output be for month 1? A) 300 units B) 350 units C) 400 units D) 450 units

Q: Use the information in Table D.1. Given the information in the optimal tableau, what is the overtime cost in dollars per unit? A) less than $12 B) greater than $12 but less than or equal to $14 C) greater than $14 but less than or equal to $16 D) greater than $16

Q: Use the information in Table D.1. Given the information in the optimal tableau, what is the inventory carrying cost, in dollars per unit per quarter? A) less than $1 B) greater than $1 but less than or equal to $2 C) greater than $2 but less than or equal to $3 D) greater than $3

Q: ________ occurs in a linear programming problem when the number of nonzero variables in the optimal solution is fewer than the number of constraints.

Q: Degeneracy occurs when the linear program model consists of only an infeasible region.

Q: The simplex method deals exclusively with corner points

Q: The simplex method is an interactive algebraic procedure for solving linear programming problems.

Q: Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four-ounce portion must contain 22 units of protein, 15 units of vitamin A, and 8 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 6 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 8 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 8 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 5 cents per ounce, and eggs cost 12 cents per ounce. To make the production process as easy as possible, she would like to make exactly four ounces of cat food from her recipe. She used POM for Windows and received the following results. Provide an interpretation.

Q: A small oil company has a refining budget of $200,000 and would like to determine the optimal production plan for profitability. The following table lists the costs associated with its three products. Marketing has a budget of $50,000, and the company has 750,000 gallons of crude oil available. Each gallon of gasoline contributes 14 cents of profits, heating oil provides 10 cents, and plastic resin 30 cents per unit. The refining process results in a ratio of two units of heating oil for each unit of gasoline produced. This problem has been modeled as a linear programming problem and solved on the computer. The set up and output follows: a. Give a linear programming formulation for this problem. Make the variable definitions and constraints line up with the computer output. b. What product mix maximizes the profit for the company using its limited resources? c. How much plastic resin is produced if profits are maximized? d. Give a full explanation of the meaning of the three numbers listed following. First Number: Slack or surplus of 42,500 for the #2 Marketing Budget constraint. Second Number: Shadow price of 0 for the #1 Refining Budget constraint. Third Number: An upper limit of "infinity" for the right-hand-side value for the #1 Refining Budget constraint.

Q: A very confused manager is reading a two-page report given to him by his student intern. "She told me that she had my problem solved, gave me this, and then said she was off to her production management course," he whined. "I gave her my best estimates of my on-hand inventories and requirements to produce, but what if my numbers are slightly off? I recognize the names of our four models W, X, Y, and Z, but that's about it. Can you figure out what I'm supposed to do and why?" You take the report from his hands and note that it is the answer report and the sensitivity report from Excel's solver routine. Explain each of the highlighted cells in layman's terms and tell the manager what they mean in relation to his problem.

Q: Briefly describe the meaning of a shadow price. Provide an example of how a manager could use information about shadow prices to improve operations?

Q: You observe a linear programming problem that has been solved using the graphical method of linear programming. The feasible region and optimal solution are clearly labeled. How could you identify the slack or surplus amounts in the scenario?

Q: What are the limitations of the graphical method of linear programming?

Q: In a linear programming model formulation, what is the meaning of a slack or surplus variable?

Q: In a linear programming model formulation, what does the feasible region represent?

Q: The interval over which the right-hand-side parameter of a constraint can vary while its shadow price remains valid is the ________.

Q: A(n) ________ is the marginal improvement in the objective function value caused by relaxing a constraint by one unit.

Q: For an "equal" constraint, only points ________ are feasible solutions.

Q: The ________ is the upper and lower limit of an objective function coefficient over which the optimal values of the decision variables remain unchanged.

Q: A modeler is limited to two or fewer decision variables when using the ________.

Q: ________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.

Q: ________ is the amount by which the left-hand side falls short of the right-hand side in a linear programming model.

Q: A(n) ________ limits the ability to improve the objective function.

Q: In linear programming, a(n) ________ is a point that lies at the intersection of two (or possibly more) constraint lines on the boundary of the feasible region.

Q: While glancing over the sensitivity report, you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours. If your original right hand value for stitching labor was 30 hours, you know that: A) the next worker that offers to work an extra 8 hours should receive at least $80. B) you can send someone home 6 hours early and still pay them the $60 they would have earned while on the clock. C) you would be willing pay up to $60 for someone to work another 6 hours. D) you would lose $80 if one of your workers missed an entire 8 hour shift.

Q: You are faced with a linear programming objective function of: Max P = $20X + $30Y and constraints of: 3X + 4Y = 24 (Constraint A) 5X - Y = 18 (Constraint B) You discover that the shadow price for Constraint A is 7.5 and the shadow price for Constraint B is 0. Which of these statements is true? A) You can change quantities of X and Y at no cost for Constraint B. B) For every additional unit of the objective function you create, you lose 0 units of B. C) For every additional unit of the objective function you create, the price of A rises by $7.50. D) The most you would want to pay for an additional unit of A would be $7.50.

Q: A manager is interested in deciding production quantities for products A, B, and C. He has an inventory of 20 tons each of raw materials 1, 2, 3, and 4 that are used in the production of products A, B, and C. He can further assume that he can sell all of what he makes. Which of the following statements is correct? A) The manager has four decision variables. B) The manager has three constraints. C) The manager has three decision variables. D) The manager can solve this problem graphically.

Q: Consider a corner point to a linear programming problem, which lies at the intersection of the following two constraints: 6X1 + 15X2< 390 2X1 + X2< 50 Which of the following statements about the corner point is true? A) X1< 21 B) X1> 25 C) X1< 10 D) X1> 17

Q: For the line that has the equation 4X1 + 8X2 = 88, an axis intercept is: A) (0, 22). B) (6, 0). C) (6, 22). D) (0, 11).

Q: An equality constraint requires that only the points on the line described by the constraint are feasible.

Q: The terms slack and surplus both refer to having too much of a resource.

Q: A binding constraint has slack but does not have surplus.

Q: When plotting constraints, it is best to ignore the inequality aspect of the equation.

Q: The graphical method is a practical method for solving product mix problems of any size, provided the decision maker has sufficient quantities of graph paper.

Q: Only corner points should be considered for the optimal solution to a linear programming problem.

Q: Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table. Fan A Fan B Fan C Component # Needed # Needed # Needed Current Inventory Wire 1 2 3 500 Nuts 8 12 14 700 Bolts 8 12 14 700 Motor 1 1 2 200 Blades 5 6 7 400 Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Milo Belsky decided to arrive at an optimal production quantity using linear programming. His initial solution was to produce 50 Fan As and 21.4 Fan Cs for a profit of $1,542.86. Determine what his inventory would be. Charlie Belsky made an important change to the model and ran the linear programming software again, His solution was to produce 50 Fan As, -150 Fan Bs, and 150 Fan Cs for a profit of $1,650 units. What change did he make to the model and what would the ending inventory be if they were to produce according to this plan? What are the practical implications of this solution?

Q: Belsky Manufacturing makes three models of fans, identified by the unimaginative names of A, B, and C. The fans are made out of nuts, bolts, wire, blades, and motors. The current inventory levels and parts list for each type of fan is shown in the table. Fan A Fan B Fan C Component # Needed # Needed # Needed Current Inventory Wire 1 2 3 500 Nuts 8 12 14 700 Bolts 8 12 14 700 Motor 1 1 2 200 Blades 5 6 7 400 Fan A sells for $18, Fan B sells for $25, and Fan C sells for $30. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Q: Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible. She has decided to make her own cat food and has the following nutritional guidelines. Each four ounce portion must contain 22 units of protein, 15 units of vitamin A, and 8 units of vitamin B. She has eggs, tomatoes, and chicken meat as possible inputs to her cat food. Each ounce of eggs contains 6 units of protein, 4 units of Vitamin A, and 3 units of Vitamin B. Each ounce of tomatoes contains 1 unit of protein, 8 units of Vitamin A, and 14 units of Vitamin B. Each ounce of chicken contains 22 units of protein, 14 units of Vitamin A, and 8 units of Vitamin B. Chicken costs 40 cents per ounce, tomatoes cost 5 cents per ounce, and eggs cost 12 cents per ounce. To make the production process as easy as possible, she would like to make exactly four ounces of cat food from her recipe. Formulate this decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Q: A portfolio manager is trying to balance investments between bonds, stocks and cash. The return on stocks is 12 percent, 9 percent on bonds, and 3 percent on cash. The total portfolio is $1 billion, and he or she must keep 10 percent in cash in accordance with company policy. The fund's prospectus promises that stocks cannot exceed 75 percent of the portfolio, and the ratio of stocks to bonds must equal two. Formulate this investment decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Q: NYNEX must schedule round-the-clock coverage for its telephone operators. To keep the number of different shifts down to a manageable level, it has only four different shifts. Operators work eight-hour shifts and can begin work at either midnight, 8 a.m., noon, or 4 p.m. Operators are needed according to the following demand pattern, given in four-hour time blocks. Time Period Operators Needed midnight to 4 a.m. 4 4 a.m. to 8 a.m. 6 8 a.m. to noon 90 Noon to 4 p.m. 85 4 p.m. to 8 p.m. 55 8 p.m. to midnight 20 Formulate this scheduling decision as a linear programming problem, defining fully your decision variables and then giving the objective function and constraints.

Q: A producer has three products, A, B, and C, which are composed from many of the same raw materials and subassemblies by the same skilled workforce. Each unit of product A uses 15 units of raw material X, a single purge system subassembly, a case, a power cord, three labor hours in the assembly department, and one labor hour in the finishing department. Each unit of product B uses 10 units of raw material X, five units of raw material Y, two purge system subassemblies, a case, a power cord, five labor hours in the assembly department, and 90 minutes in the finishing department. Each unit of product C uses five units of raw material X, 25 units of raw material Y, two purge system subassemblies, a case, a power cord, seven labor hours in the assembly department, and three labor hours in the finishing department. Labor between the assembly and finishing departments is not transferable, but workers within each department work on any of the three products. There are three full-time (40 hours/week) workers in the assembly department and one full-time and one half-time (20 hours/week) worker in the finishing department. At the start of this week, the company has 300 units of raw material X, 400 units of raw material Y, 60 purge system subassemblies, 40 cases, and 50 power cords in inventory. No additional deliveries of raw materials are expected this week. There is a $90 profit on product A, a $120 profit on product B, and a $150 profit on product C. The operations manager doesn't have any firm orders, but would like to make at least five of each product so he can have the products on the shelf in case a customer wanders in off the street. Formulate the objective function and all constraints, and clearly identify each constraint by the name of the resource or condition it represents.

Q: The ________ problem is a one-period type of aggregate planning problem, the solution of which yields optimal output quantities of a group of products or services, subject to resource capacity and market demand conditions.

Q: Referring to Scenario D.1, assume that an optimal serving contains 0.89 ounces of chicken and 0.52 ounces of tomatoes. Which of the following statements is best? A) The serving costs about 20 cents. B) The serving costs about 30 cents C) The serving costs about 40 cents. D) The serving costs about 50 cents.

Q: Referring to Scenario D.1, which of the following statements is best? A) Making the cat food out of only eggs is optimal B) Making the cat food out of only eggs is less expensive than making it out of only tomatoes. C) Making the cat food out of only eggs means that the Vitamin B constraint would not be satisfied. D) Making the cat food out of only chicken means the Vitamin B constraint would not be satisfied.

Q: Referring to Scenario D.1, what is an appropriate constraint for this scenario? A) 4*Eggs + 8*Tomatoes + 14*Chicken ≤ 15 B) 5*Eggs + 1*Tomatoes + 22*Chicken ≥ 20 C) 4*Eggs + 8*Tomatoes + 14*Chicken = 15 D) 15*VitaminA = Eggs + Tomatoes + Chicken

Q: Referring to Scenario D.1, what is an appropriate constraint for this scenario? A) 4*Eggs + 5*Tomatoes + 14*Chicken ≥ 15 B) 22*Protein + 15*VitaminA + 8*VitaminB ≥ 8 C) .12*Egg + .5*Tomato + .4*Chicken ≥ 4 D) 22*Protein + 15*VitaminA + 8*VitaminB ≥ 4

Q: Referring to Scenario D.1, what is an appropriate objective function for this scenario? A) Max Z = .12*Egg + .08*Tomato + .4*Chicken B) Max Z = 20*Protein + 15*VitaminA + 10*VitaminB C) Min Z = .12*Egg + .08*Tomato + .4*Chicken D) Min Z = 20*Protein + 15*VitaminA + 10*VitaminB

Q: In a linear programming model, the objective function answers the question What is to be maximized?

Q: A manufacturer builds finished items A, B, and C from five different components. They currently have several finished units, a number of items that are partially complete, and many components that have just been delivered from their suppliers. The finished items, incomplete items and raw components can all be assigned some monetary value even though the manufacturer typically does not sell anything except finished items. The manufacturer needs to raise capital quickly so they formulate a linear program to help them decide on the most profitable way ahead. Their linear programming expert forgets to restrict their decision variables to non-negative values and is surprised when the computer output tells them that finished item A and C should be negative. If the company always follows the advice of their linear programming analysis, what should they do and why?

Q: What are the assumptions of linear programming? Provide examples of each.

Q: The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

Q: ________ is an assumption that the decision variables must be either positive or zero.

Q: Parameters that are quantified without doubt meet the linear programming assumption of ________.

Q: A(n) ________ is a value that the decision maker cannot control and that does not change when the solution is implemented.

Q: The ________ represents all permissible combinations of the decision variables in a linear programming model.

Q: In a linear program, ________ are the limitations that restrict the permissible choices for the decision variables.

Q: In a linear program, ________ represent choices the decision maker can control.

Q: The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

Q: ________ is useful for allocating scarce resources among competing demands.