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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 3,999 pounds $ 24 per pound 4,000 pounds or more $ 23 per pound The cost to place an order is $40. Annual demand is 2,700 units. Holding (or carrying) cost is 25 percent of the material price. What is the economic order quantity to buy each time, and its total cost

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jepessoa

Answer:

EOQ = 201 units

total cost = $66,007.35

Explanation:

we can calculate the EOQ using 2 different prices (it makes no sense to use $23 since the minimum order size is larger than annual demand):

EOQ = √[(2 x S x D) / H]

  • S = order cost
  • D = annual demand
  • H = holding cost

$25 per unit

S = $45

D = 2,700

H = $25 x 25% = $6.25

EOQ = √[(2 x 45 x 2,700) / 6.25] = 197.18

$24 per unit

S = $45

D = 2,700

H = $24 x 25% = $6

EOQ = √[(2 x 45 x 2,700) / 6] = 201.25 ≈ 201 units

since both EOQs are higher than 100 units, then we must use $24 per unit

you have to make 2,700 / 201 = 13.43

total cost = (13.43 x $45) + (2,700 x $24) + (201 x $6 x 0.5) = $604.35 + $64,800 + $603 = $66,007.35