Midterm2015.docx - Student number Queens University School...

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Student number:______________________________ Queen’s University School of Business Business Decision Modeling COMM 163 FALL 2015 Mid Term Examination – October 20, 2015 1. Marks are as indicated and total 100. 2. Time allowed – 2 hours. 3. Write in the space provided. If you find space to be insufficient, write on the back of the previous page and clearly indicate that you have done so. 4. Calculators are permitted. 5. Answer all questions. 6. Write your student number on every page in the space provided The candidate is urged to submit with the answer paper a clear statement of any assumptions made if doubt exists as to the interpretation of any question that requires a written answer. Question Marks Marks earned 1 30 _______ 2 35 _______ 3 35 _______ Instructors: P. Roman R. Wright Page 1 of 10
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Student number:______________________________ Question One (30 Marks) You are in charge of loading cargo ships for International Cargo Company (ICC) at a major east coast port. You have been asked to prepare a loading plan for an ICC freighter bound for Africa. An agriculture commodities dealer would like to ship the following commodities aboard the ship. Commodity Tons Available Volume per Ton (cubic feet) Profit per Ton ($) 1 4,000 40 70 2 3,000 25 50 3 2,000 60 60 4 1,000 50 80 You can elect to load any or all of the available commodities but the ship has three cargo holds with the following restrictions. Cargo Hold Weight Capacity (tons) Volume Capacity (cubic feet) Forward 3,000 100,000 Centre 5,000 150,000 Rear 2,000 120,000 More than one type of commodity can be paced in the same cargo hold but because of weight and balance restrictions, the weight in the forward hold must be within 10% of the weight in the rear hold and the centre hold must be within 40% to 60% of the total weight on board. Formulate a linear model to maximize profit. Give clear definitions to your decision variables. DO NOT attempt to solve. Page 2 of 10
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Student number:______________________________ Cargo loading (35 Marks) Decision variables: Let x ij be the tons of commodity i ( i = 1,2,3 , 4 ) put in cargo hold j = 1 ( forward ) , 2 ( centre ) , 3 ( rear ) j ¿ . Objective function: Max 70 j = 1 3 x 1 j + 50 j = 1 3 x 2 j + 60 j = 1 3 x 3 j + 80 j = 1 3 x 4 j Constraints: Commodity amount: Commodity 1: j = 1 3 x 1 j 4000 Commodity 2: j = 1 3 x 2 j 3000 Commodity 3: j = 1 3 x 3 j 2000 Commodity 4: j = 1 3 x 4 j 1000 Weight: Forward hold: i = 1 4 x i 1
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