IE 168 Q3 Take-Home

IE 168 Q3 Take-Home - Problems for Section 4.8 26 A local...

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Unformatted text preview: Problems for Section 4.8 26. A local outdoor vegetable stand has exactly 1,000 square feet of Space to display 27. 28. . three vegetables: tomatoes, lettuce, and zucchini. The appropriate data ~for these _ items are given in the following table. 'ltem Tomatoes Lettuce Zucchini WW Annual demand 850 1,280 630 (in pounds) . ‘ ‘ ' Cost per pound $0.29; ‘ $0.45 $0.25 M The setup cost for replenishment ofthe vegetables is $100 in each case, and the space consumed by each vegetable is proportional to its costs, with tomatoes re~ quiring 0.5 square foot per pound. The annual interest rate used for computing holding costs is 25 percent. What are the’ optimal quantities that should be pur— chased of these three vegetables? Suppose that the vegetabies discussed in Problem 26 are purchased at difierent times. In what way could that have an effect on the order poiicy that the stand owner Should use? Suppose that in Problem 26 the space consumed by each vegetable is not proportional to its cost In particular, suppose that one pound of lettuce required 0.4 square foot of space and one pound of zucchini required 1 square foot of space. Determine upper and lower bounds on the optimal values of the order quantities in this case. Test different values of the Lagrange multiplier to find the optimal val» ues of the order quantities. (A spreadsheet is ideally suited for this kind of calcu- lation. If you solve the problem using a spreadsheet, place the Lagrange multiplier in a cell so that its value can be changed easily.) ...
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