Linear Programming Exercises-1

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University of Illinois, Urbana Champaign *

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MISC

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Industrial Engineering

Date

Feb 20, 2024

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docx

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3

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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
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