A particular raw material is available to a company at three different prices, d

ID: 449784 • Letter: A

Question

A particular raw material is available to a company at three different prices, depending on the size of the order

Less than 100 pounds $ 25 per pound
100 pounds to 2,999 pounds $ 24 per pound
3,000 pounds or more $ 23 per pound

The cost to place an order is $60. Annual demand is 3,100 units. Holding (or carrying) cost is 20 percent of the material price.

What is the economic order quantity to buy each time, and its total cost? (Round your answers to the nearest whole number.)

Economic order quantity _____ pounds

Total cost $ _______

D = 3100

Co = $60

H = 20% = 0.2

When C = $25

EOQ = Sqrt((2 * D * Co)/(H*C)) = Sqrt((2 * 3100 * 60)/(0.2*25)) = 272.7636

It is not the EOQ, As it does not lies in the range (0 – 100).

When C = $24

EOQ = Sqrt((2 * D * Co)/(H*C)) = Sqrt((2 * 3100 * 60)/(0.2*24)) = 278.3882 = 278 UNITS

It is the EOQ, As it lies in the range (100 - 2999).

Now Calculate the Total Cost for each cost level.

TC = (D* C) + ((D/Q)*Co) + (Q/2)*C*H))

When C = $24, Q = EOQ = 278

TC = (3100*24) + ((3100/278)*60) + ((278/2)*0.2*24) = $ 75736.26

When C = $23, Q = 3000

TC = (3100*23) + ((3100/3000)*60) + ((3000/2)*0.2*23) = $ 78262

Comparing total cost we get that

EOQ = 278 units

Total Cost = $ 75736.26 = $ 75736

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