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hw3.sol

# hw3.sol - IE 335 Operations Research Optimization Solutions...

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IE 335 Operations Research - Optimization Solutions to Homework 3 Spring 2012 Problem 11 Let x B , x H , x A , x P represent amounts invested in bonds, home loans, auto loans and personal loans respec- tively. max 0 . 10 x B + 0 . 16 x H + 0 . 13 x A + 0 . 20 x P s.t. x B + x H + x A + x P 500 , 000 x P x B x H x A x P 1 4 ( x B + x H + x A + x P ) x B , x H , x A , x P 0 Problem 12 Let x 5 , x 6 , . . . , x 10 represent the number of people who work 4-hour shifts starting at 5am, 6am, . . . , 10 am respectively. min 4(7( x 5 + x 6 + x 7 ) + 6( x 8 + x 9 + x 10 )) (1) s.t. x 5 2 (2) x 5 + x 6 3 (3) x 5 + x 6 + x 7 5 (4) x 5 + x 6 + x 7 + x 8 5 (5) x 6 + x 7 + x 8 + x 9 4 (6) x 7 + x 8 + x 9 + x 10 3 (7) x 8 + x 9 + x 10 2 (8) x 9 + x 10 5 (9) x 10 6 (10) x 5 , . . . , x 10 0 (11) The objective function (1) tries to minimize the total cost of the staffing plan. Each of the following constraints enforce the number of runners required for each hour. E.g. Constraint (5) ensures that from 8am-9am, we will have at least 5 runners (as required in the problem) by constraining the total number of

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