Question

4. A local outdoor vegetable stand has exactly 750 square feet of space to display 3 vegetables: tomatoes, lettuce, and zucchini. The appropriate data for these items is given in the following table. Tomatoes Lettuce Zucchini 800 1200 450 Annual Demand (in lb) Cost (per lb) Space requirement (in ft²/1b) $0.50 $0.30 $0.40 0.5 T 0.9 0.3 The setup cost for replenishment of the vegetables is $500 for each type of vegetable. The annual interest rate used for computing holding costs is 2 percent. a) Find the individual EOQs for each vegetable without regard to the display space constraint. b) What is the total display space required by the EOQ amounts in part a? c) Now consider the display space constraint; what are the optimal quantities that should be purchased of these three vegetables? d) What is the maximum amount (in $/ft) this vegetable vendor should be willing to pay for additional display space?

Answer 1

A) Calculation of Economic Order Quantity (EOQ) EOQ = 2 X Demand per Annum X ordering Cost Holding Cost Per unit Per Annum 1. Tomatoes: Given Demand per annum (lb) Ordering Cost Holding Cost per unit per annum = 800 = $ 500 = ? Holding Cost = Annual average Quantity X Cost of Purchase X Interest Rate = (800/2) X 0.50 X 2% = 400 X 0.50 X 2% = 200 X 2% = 4 EOQ = 2 X 800 X 500 EOQ = 800000 4 EOQ = 447.21 = 448 lb per order 2. lettuce: Given Demand per annum (lb) Ordering Cost Holding Cost per unit per annum = 1200 = $ 500 = ? Holding Cost = Annual average Quantity X Cost of Purchase X Interest Rate = (1200/2) X 0.30 X 2% = 600 X 0.30 X 2% = 180 X 2% = 3.6 EOQ = 2 X 1200 X 500 3.6 EOQ = 1200000 3.6 EOQ = 577.35 = 578 lb per order

3. Zucchini: Given Demand per annum (lb) Ordering Cost Holding Cost per unit per annum = 450 = $ 500 Holding Cost Annual average Quantity X Cost of Purchase X Interest Rate = (450/2) X 0.40 X 2% = 225 X 0.40 X 2% = 90 X 2% = 1.8 EOQ = 2 X 450 X 500 v 1.8 EOQ = 450000 1.8 EOQ = 500 = 500 lb per order B. Display Space required as Per EOQ Quantity Lettuce SI. No 1 Tomotoes 448 0.5 578 0.9 Zucchini 500 0.3 Particulars EOQ Space Requirement (ft/tb) Total Space required (ft) 224 520.20 150 Total Space Required by vegetable Vendor as per EOQ in "a" = 224+520.20+150 = 894.20 Square feet