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# sol5 - AMS 341 Spring 2010 Homework Set 5 — Solution...

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AMS 341 Spring, 2010 Homework Set # 5 — Solution Notes #5, 5.1: a45 a54 x 2 10 C x 1 10 A D B(20 , 10) (a) The slopes are - 1 2 for the first constraint and - 2 for the second. To keep the current basis remain optimal, the slope - c 1 2 of the isoprofit line must satisfy - 2 ≤ - c 1 2 ≤ - 1 2 . Thus, the profit from type 1 radio c 1 satisfies 1 c 1 4. The profit is equal to the price minus the cost of producing one type 1 radio, which is 22. The price of type 1 radio is between \$23 and \$26. (b) Similar to (a), suppose the profit from type 1 radio is fixed, and the profit from type 2 radio is c 2 the isoprofit line must satisfy - 2 ≤ - 3 c 2 ≤ - 1 2 . and therefore 1 . 5 c 2 6. The price of type 2 radio is between \$21.5 and \$26. (c) At point C, we have x 1 + 2 x 2 = 25. As long as laborer 1 work no less than 25 hours per week, the current basis will remain optimal. Therefore, in this problem the basis is still optimal and the new optimal solution is z = 230 3 ,x 1 = 70 3 ,x 2 = 10 3 .
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