Winona Knit (WK), a wholesaler of wool sweaters, sources the sweaters from an Io

Question

Winona Knit (WK), a wholesaler of wool sweaters, sources the sweaters from an Iowa company, Chilwool Inc. (CI), for $15 per sweater when ordered 3 months ahead of the selling season. WK’s wholesale price is $30. At the end of the selling season discount outlets buy the sweaters from WK at $13 each. WK’s demand forecast for the sweater is normally distributed with a mean of 2,500 sweaters and standard deviation of 1,200 sweaters.

If the cost of underage $12, cost of overage is $3 and WK orders 3,520 sweaters, what is WK’s approximate expected profit?

a. $30,000

b. $24,960

c. $15,040

d. $14,400

Explanation / Answer

ANSWER: b. $24,960

Solution: Given that, Mean demand, m = 2500

Standard deviation of demand, s = 1200

Underage cost, Cu = $ 12

Overage cost, Co = $ 3

Order quantity, Q = 3520

z = (Q-m)/s = (3520-2500)/1200 = 0.85

L(z) = 0.11 (taken from standard loss table)

Expected Lost sales, L(Q) = s*L(z) = 1200*0.11 = 132

Expected Sales, S(Q) = m - L(Q) = 2500-132 = 2368

Expected leftover inventory, V(Q) = Q - S(Q) = 3520 - 2368 = 1152

Expected Profit =S(Q)*Cu - V(Q)*Co = 2368*12 - 1152*3 = $ 24,960

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