A company experiences annual demand of 1,050 units for an item that it purchases
ID: 367828 • Letter: A
Question
A company experiences annual demand of 1,050 units for an item that it purchases. The rate of demand per day is very stable, with very little variation from day to day. The item costs $42 when purchased in quantities less than 240 and $40 for 240 or more. Ordering costs are $32 and the carrying cost is 25 percent.
a. What will be the total costs for each alternative? (Round your intermediate calculations and final answers to the nearest dollar amount.)
b. How much should the company buy each time an order is placed?
c. How much the company can save by placing the order? (Round your answer to the nearest dollar amount.)
Total Cost Unit Cost at $42 Unit Cost at $40Explanation / Answer
Expert Answer
[Anonymous]
Anonymousanswered this
Given Annual deand D = 1,000 units
Ordering cost S = $40
Carrying cost I = 25%
Item cost C = $50 for <100 Quantity
= $ 48 for 100 or more
[EOQ=sqrt{2DS/IC}]
C = $50
[EOQ=sqrt{(2*1000*40)/(.25*50)}]
= 80 Units ( Feasible)
C = $48
[EOQ=sqrt{(2*1000*40)/(.25*48)}]
= 81.64 (which is not feasible)
If we order at C = $50 we dont get discount. So we calculate total cost at Q = 80 and Q = 100
Total cost = CD + (Q/2)(IC) + (D/Q)S
At C = 50 and Q = 80
Total cost = (50*1000) + (80/2)(.25*50) + (1000/80)40
= 50,000 + 500 + 500
= $ 51,000
At C = 48 and Q = 100
Total cost = (48*1000) + (100/2)(.25*48) + (1000/100)40
= 48,000 + 600 + 400
= $49,000
Total cost is less for Quantity for 100 at 48 when compare with Quantity for 80 at 50. So company should buy 100 units each time an order is placed
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