DISCOUNT PROBLEM: A supplier is willing to give you a price discount if you boug
ID: 434301 • Letter: D
Question
DISCOUNT PROBLEM: A supplier is willing to give you a price discount if you bought in bulk as shown below. Assume a monthly demand of 500 units of the product. The cost to place an order is $50 per order, and it costs 25% of unit price to hold the product in inventory for one year.
a.) What is the valid EOQ corresponding to the volume range of 150-349 units of the product?
b.) What is the optimal EOQ (corresponding to the least total cost)?
c.) What is the least total cost at the valid EOQ?
Number of Units Price per Unit 1-149 14.10 150-349 13.90 350 and more 13.70Explanation / Answer
Annual demand, D = 500*12 = 6000 units
Order cost, S = $ 50
a) Valid price for volume range of 150-349 units, C = 13.90
Holding cost, H = 13.90*0.25 = 3.475
EOQ = SQRT(2DS/H) = SQRT(2*6000*50/3.475) = 416
The applicable price for this quantity is 13.70
Holding cost, H = 13.70*0.25 = 3.425
Valid EOQ = SQRT(2DS/H) = SQRT(2*6000*50/3.425) = 419
b) Total cost is lowest at EOQ of 419
c) Least total cost = (D/Q)*S + (Q/2)*H + D*C
= (6000/419)*50 + (419/2)*3.425 + 6000*13.7
= $ 83,633
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