Suppose that in the given problem 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 values of the order quantities. (A spreadsheet is ideally suited for this kind of calculation. If you solve the problem using a spreadsheet, place the Lagrange multiplier in a cell so that its value can be changed easily.) A local outdoor vegetable stand has exactly 1,000 square feet of space to displaythree vegetables: tomatoes, lettuce, and zucchini. The appropriate data for theseitems are given in the following table.ItemTomatoesLettuceZucchiniAnnual demand8501,280630(in pounds)Cost per pound$0.29$0.45$0.25The setup cost for replenishment of the vegetables is $100 in each case, and thespace 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 computingholding costs is 25 percent. What are the optimal quantities that should be pur-chased of these three vegetables?

Optimal quantities to be purchased for the three vegetables are shown in the steps below: Step1:…

Answered: A local outdoor vegetable stand has…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Suppose that in the given problem 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 values of the order quantities. (A spreadsheet is ideally suited for this kind of calculation. If you solve the problem using a spreadsheet, place the Lagrange multiplier in a cell so that its value can be changed easily.)

A local outdoor vegetable stand has exactly 1,000 square feet of space to display
three vegetables: tomatoes, lettuce, and zucchini. The appropriate data for these
items are given in the following table.
Item
Tomatoes
Lettuce
Zucchini
Annual demand
850
1,280
630
(in pounds)
Cost per pound
$0.29
$0.45
$0.25
The setup cost for replenishment of the 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?

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