3) (20pts) A regional wholesaler of a certain gadget has demand forecasts for th

Question

3) (20pts) A regional wholesaler of a certain gadget has demand forecasts for the coming 4 weeks. Gadgets are purchased at 35 liras per item. Order cost for making a purchase in any week is 850 liras. Inventory holding cost of is 7 liras per item per week. Demand should be met with no backorders and there is no upper limit for the amount of gadgets purchased per week Week Demand 90 110 50 150 Determine the optimal purchasing quantities for weeks 1, 2, 3, and 4. Exactly state the values of Pi, P2, Ps, and Ps. What is the cost of the optimal solution?

Explanation / Answer

Variable

Pi: Purchase quantity in week i

Constraints

1. Demand for every week should meet : Di < Pi

2. Pi are non negative integers

Objective

Minimum cost : (P1+P2+P3+P4)*35 + inventory holding cost + ordering cost

Solution

so optimal quantities of purchase are 190, 160, 0 and 150

Week purchase demand total available constr (aval.>demand) purchase cost inventory cost order cost 1 190 190 190 0 6650 0 850 2 160 110 160 50 5600 350 850 3 0 50 50 0 0 0 0 4 150 150 150 0 5250 0 850 Total individual costs 17500 350 2550 Total cost 20400

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