Linear Programming Exercises-1
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School
University of Illinois, Urbana Champaign *
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Course
MISC
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
3
Uploaded by JusticeInternetSeahorse45
Southern California Chemical Company
manufactures two industrial chemical products, called kreolite-red and kreolite-blue. Two machines are used in the process, and each machine has 24 hours of capacity per day. The following data are available:
Kreolite-Red
Kreolite-Blue
Selling price per drum
$
36
$
42
Variable cost per drum
$
28
$
28
Hours required per drum on machine I
2
hr.
2
hr.
Hours required per drum on machine II
1
hr.
3
hr.
The company can produce and sell partially full drums of each chemical. For example, a half drum of kreolite-red sells for $18.
Required:
1.
Formulate the product-mix problem as a linear program, assuming X, Y ≥ 0. X denotes Kreolite-Red and Y denotes Kreolite-Blue.
-
Objective function
-
Constraint equations
-
Decision variables
2.
Determine the value of the objective function value at the optimal solution by solving the problem in excel using SOLVER.
3
. What is the maximum increase in the Kreolite-Blue’s variable cost per drum while maintaining the current optimal solution?
Deru Chocolate Company
manufactures two popular candy bars, the Venus bar and the Comet bar. Both candy bars go through a mixing operation where the various ingredients are combined, and the Coating Department where the bars from the Mixing Department are coated with chocolate. The Venus bar is coated with both white and dark chocolate to produce a swirled effect. A material shortage of an ingredient in the Comet bar limits production to 300 batches per
day. Production and sales data are presented in the following table. Both candy bars are produced
in batches of 200 bars.
Use of Capacity in Hours per Batch of Product
Department
Available Daily
Capacity in Hours
Venus
Comet
Mixing
525
1.5
1.5
Coating
500
2.0
1.0
Management believes that Deru Chocolate can sell all of its daily production of both the Venus and Comet bars. Other data follow.
Venus
Comet
Selling price per batch
$300
$350
Variable cost per batch
100
225
Monthly fixed costs (allocated evenly between both products)
375,000 375,000
Required:
1.
Complete the following equations: (1) objective function and (2) all constraints 2.
How many batches of each type of candy bar (Venus and Comet) should be produced to maximize the total contribution margin?
3.
Calculate the contribution margin at the optimal solution.
4. how would the solution change if there was no material shortage for Comet bar ingredients
Meals for Professionals, Inc
., offers monthly service plans providing prepared meals that are delivered to the customers’ homes. The target market for these meal plans includes double-
income families with no children and retired couples in upper income brackets. The firm offers two monthly plans: Premier Cuisine and Haute Cuisine. The Premier Cuisine plan provides frozen meals that are delivered twice each month; this plan generates a contribution margin of $120 for each monthly plan sold. The Haute Cuisine plan provides freshly prepared meals delivered on a daily basis and generates a contribution margin of $90 for each monthly plan sold.
The company’s reputation provides a market that will purchase all the meals that can be prepared. All meals go through food preparation and cooking steps in the company’s kitchens. After these steps, the Premier Cuisine meals are flash frozen. The time requirements per monthly
meal plan and hours available per month are as follows:
Preparation Cooking Freezing
Hours required:
Premier Cuisine
2
2
1
Haute Cuisine
1
3
0
Hours available
60
120
45
For planning purposes, Meals for Professionals, Inc., uses linear programming to determine the most profitable number of Premier Cuisine and Haute Cuisine monthly meal plans to produce.
Required:
1.
State the objective function and the constraints that management should use to maximize the total contribution margin generated by the monthly meal plans.
2.
Determine the optimal solution to the company's production planning problem in terms of the number of each type of meal plan to produce.
3.
Calculate the value of the objective function at the optimal solution.
4. Given the Sensitivity Report, how much do you believe we can rely on this optimal solution?
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