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Question
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.
Answer
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Related questions
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Consider the following problems in which four jobs must each be processed on two machines starting with Machine A and then going to Machine B. The following processing times are available (in hours): Job
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Q:
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B
C
D 1
$5
$10
$5
$4 2
$3
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$3 3
$8
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$2 4
$2
$3
$5
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Location 1: 600
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What is the lowest-cost shipping arrangement that can be made between the plant locations and distributors and what is the annual shipping cost?
Q:
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Q:
Complete the following MPS Record
Q:
Consider the MPS, BOM, and inventory data shown.
Master Production Schedule:
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1
2
3
4
5
6
7
8
9
10 Finished Item A MPS Start
20 40
30 20 40 Bill of Material:
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Lead Time
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L4L
1
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2 40 D
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1 100 E
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Q:
Job
Process Time (days)
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Days Since Arrival A
2
7
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8
16
9 C
4
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8 D
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17
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18
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Q:
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1
2
3
4
5
6 Requirement
7
8
9
11
12
7 Costs associated with operations are as follows:
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Q:
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Q:
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Q:
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Q:
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71.9
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70.3
74.2
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Q:
Develop a process chart for one of the following:
1) Researching and writing a paper for your Operations Management class
2) Managing, developing and completing a team project for a Finance (or other) class
3) Planning for your job interview process as you approach graduation (including resume preparation, developing interview skills, researching company backgrounds, etc.)
4) Studying and developing a process improvement plan for a business or other process you are familiar with (e.g., fast food restaurant, obtaining tickets to a university-sponsored event, dry cleaners, book purchases for next term, and the like)
Q:
Develop a process chart for a manual car wash.
Q:
Because a telephone customer service center has experienced several problems, it has begun to analyze the data from customer complaints. The first step was to construct the following table. Use this data to build a Pareto chart to help identify the "vital few" problems. Process Failure
Total Failures Person not available
5 Incorrect information given
12 Phone line busy
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20 People unfriendly
17
Q:
Job
Process Time (days)
Due Time (days)
Days Since Arrival A
2
7
12 B
8
16
9 C
4
4
8 D
10
17
5 E
5
15
3 F
12
18
2 Use the information in the preceding table and sequence the six jobs using FCFS and EDD. The jobs are listed in the order of their arrival. Calculate the average flow time and average past due. It is now time zero.
Q:
The estimated time to produce the first unit is 100 hours. If a 90 percent learning rate is applicable, what is the estimated time of producing the first ten units? Refer to the copy of Table I.1 appended to this exam.
Q:
A single-sampling plan by attributes is needed for a purchased component. Table G.1 is appended to this exam.
Sample size = 80
Acceptance number (c) = 1
Acceptance quality level (AQL) = 0.02
Lot tolerance proportion defective (LTPD) = 0.06
Given the preceding information, draw the OC curve for this plan.
Q:
Refer to the bank process model. The bank's process improvement group has developed a number of process and technology changes that will improve the Teller's process rate per customer from a mean of 3.0 minutes to 2.5 minutes (standard deviation remains at 0.5 minutes). The Bank Manager wants to determine if the improved process rate, along with the special promotion for new customers, will allow the "arrive and immediately leave" rate and average customer wait time in line achieved to still be met (12% balk rate, 9.95 minutes in line). If so, the manager will implement the process and technology changes and allow the special promotion to proceed. Using SimQuick, estimate the new arrive and immediately leave rate and average time in line. What decision should the manager make?
Q:
Walter White must satisfy an annual demand of 50,000 pounds per year. The setup cost for each batch is $6,500 and once the setup is complete, the product may be produced at the rate of 1800 pounds per day. There is a holding cost of $15 per unit per year and the plant operates on a 350-day production year. How big should the production batch be and how long (in days) will it take to produce the batch?
Q:
SimQuick is to be used to simulate the following bank process: Customers arrive at the Entrance Door of the bank with an average time between arrivals of 2.5 minutes. The Line Buffer holds 6 customers. If a customer arrives and the buffer line is filled, the customer leaves. The Work Station Teller's processing time per customer is normally distributed, with a mean of 3.0 minutes and a standard deviation of 0.5 minutes. The Served Customer Buffer in the flowchart is used to count the number of customers processed during the simulation period. A 2-hour period is to be simulated and the simulation should be repeated 30 times. Determine:
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b) The percentage of customers who arrived at the bank and left because the buffer line was full;
c) The utilization of the teller (% of time working) during the 2-hour period;
Q:
What is degeneracy in the context of linear programming? Why is degeneracy a concern?
Q:
Construct a 3-sigma and R-chart for the length in centimeters of a part from the following table. Sample #
Observation 1
Observation 2
Observation 3
Observation 4 1
0.486
0.499
0.493
0.511 2
0.499
0.506
0.516
0.494 3
0.496
0.5
0.515
0.488 4
0.495
0.506
0.483
0.487 5
0.472
0.502
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0.469 6
0.473
0.495
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0.493 7
0.495
0.512
0.49
0.471 8
0.525
0.501
0.498
0.474 9
0.497
0.501
0.517
0.506 10
0.495
0.505
0.516
0.511
Q:
The three-person crew worked their way through the neighborhood, testing doorknobs and windows and slipping past security systems like a team of ninjas. Of course, they weren't ninjas, but a crew of brazen burglars, hoping to grab cash and other valuables to fence at the next level of their supply chain. Fortune smiles on them on this day in the prestigious Edmond Oaks neighborhood. A lawn maintenance crew is creating a tremendous racket mowing and edging lawns, which completely drowns out the sounds of breaking glass. Details of the day's haul appear in Table C.
a. What is the multifactor productivity?
b. What is the labor productivity?
Table C: The Haul ITEM
SALES PRICE
LABOR
MATERIAL Krugerrand
$1,500
1 hr
$2 Flat screen TV
$250
.25
$1 $200 cash
$200
.05
$45 Lava lamp
$5
.15
$25 Rolex watch
$180
.10
$1 Workers are paid at a flat rate of 20% of the sales price of the merchandise. Materials cost
represents the cost of gasoline and surgical gloves, and overhead is 20% of the sales price of
the merchandise.
Q:
Consider this list of jobs that have just arrived and are ready for processing. They all require processing first on machine 1 and then on machine 2. Both machines are now idle. Develop a schedule that minimizes makespan and calculate this makespan time. Now assume that each job can be split into two jobs, each having half the duration on both machine 1 and machine 2. Using the original sequence that minimized average flow time, calculate the flow times for all split jobs What is the effect of this new schedule on the average flow time for these split jobs? Job
Machine 1
Machine 2 1
14
6 2
11
12 3
16
14 4
12
8 5
22
9 6
13
15 7
10
12 8
8
13