Question

a mail-order house uses 15,875 boxes a year. carrying costs are 79 cents per box a year, and ordering costs are $97. the following price schedule applies. number of boxesprice per box 1,000 to 1,999 $1.45 2,000 to 4,999 1.35 5,000 to 9,999 1.25 10,000 or more 1.20

Answer 1

Number of boxes price per box according to price schedule is 3.18 orders.

Given

Annual demand D = 15875 boxes per year

Carrying cost H = 0.79 cents

Ordering cost S = $97

Optimal order quantity Q

Q=$\sqrt{\frac{2*15875*97}{0.79}}$

Q = 1974 units

But at Q = 1974 units we are getting less discount. So, we calculate total cost at Q = 19, Q = 2000, Q = 5000, Q = 10000

Total cost = Purchase cost + Annual Holding cost + Annual ordering cost = PD + (Q/2)H + (D/Q)S

The total cost is less at optimal order quantity Q = 5000

a) Optimal order quantity = 5000 boxes

b) Number of orders = (D/Q) = 15875/5000 = 3.18

Number of orders = 3.18 orders

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