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Unformatted text preview: UNIVERSITY OF WATERLOO MIDTERM EXAMINATION FALL TERM 2011 Student Name (Print Legibly) ( family name ) ( given name ) Signature Student ID Number COURSE NUMBER CO 227 COURSE TITLE Introduction to Optimization COURSE SECTION 001 DATE OF EXAM Wednesday, November 2, 2011 TIME PERIOD 7:00  9:00 pm DURATION OF EXAM 2 hours NUMBER OF EXAM PAGES (Including cover page) 12 pages INSTRUCTORS P. Roh EXAM TYPE Closed Book ADDITIONAL MATERIALS ALLOWED Calculator (Nongraphing) Notes: 1. Fill in your name, ID number, and sign the paper. 2. Answer all questions in the space provided. Ask the proctor for ex tra blank pages if necessary. Show your work and give FORMAL solu tions. Leave your answers in exact form, such as 5 + √ 7, 4 1 / 3 sin( 3 10 ), etc. 3. Check that the examination has 12 pages. 4. Your grade will be influenced by how clearly you express your ideas, and how well you organize your solutions. Marking Scheme: Question Mark Out of 1 16 2 10 3 15 4 19 5 10 Total 70 DO NOT WRITE FORMULAS ON THE COVER PAGE. CO 227  Midterm Examination Fall 2011 Page 2 of 12 1. For these questions, write a mathematical program to solve the given problem and classify the type of mathematical program as linear, integer, or nonlinear. (Include an explanation of what each variable in your program represents.) (a) CrApple is a company that produces cheap cellphones. Each phone requires 3 differ ent parts. Each phone requires 4 units of part 1, 1 unit of part 2, and 2 units of part 3. CrApple has 2 factories to makes the parts. Their production lines are setup to makes all 3 parts at the same time but each factory produces different amounts per hour: Part 1 Part 2 Part 3 Factory A 83 18 51 Factory B 62 21 41 (So factory A in one hour makes 83 units of part 1, 18 units of part 2, AND 51 units of part 3.) Factory A costs $3,000/hr to operate and Factory B costs $1,600/hr to operate. Each factory can run for 20 hr/day. Labour contracts require that if an hour of production has started, it must be completed. The CEO of CrApple wants parts for 800 phones made per day. Any excess parts produced each day cannot be used the next day and must be disposed of. It costs $3 for part 1, $4 for part 2, and $5 for part 3 in disposal costs. What should the company do to minimize cost each day? Solution: Let x A ,x B be the number of hours that factory A and B operate. The mathematical program is: miminize 3000 x A + 1600 x B + 3 83 x A + 62 x B 800 + 4 18 x A + 21 x B 800 +5 51 x A + 41 x B 800 subject to 83 x A + 62 x B ≥ 3200 18 x A + 21 x B ≥ 800 51 x A + 41 x B ≥ 1600 x A ≤ 20 x B ≤ 20 x A ,x B ≥ x A ,x B integer This is an integer program. CO 227  Midterm Examination Fall 2011 Page 3 of 12 (b) Red Cow is a company that makes energy drinks. They have 3 machines to make the secret ingredients for their signature beverage. Their beverage has two secret ingredients. Each L of beverage requires 50g of ingredient A and 100g of ingredient B. Each machine produces different amounts of each ingredient (at the same time)B....
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 Fall '08
 Burbidge,John
 Optimization, LP, Midterm Examination, Canonical form

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