A buyer for a department store orders sweaters about 6 months before the winter season. The store plans to hold a March clearance sale to sell any surplus goods by February 29. Each piece costs $100 per pair and sells for $120 per pair. At the sale price of $60 per pair, it is expected that any remaining stock can be sold during the March sale. Assume that a uniform probability distribution ranging from 250 to 450 items describes the demand. The expected demand is 300. In the context of the single period inventory system, the optimal order size Qmust satisfy the condition _____.
A) P(demand $\leq$ Q*) = 1/2
B) P(demand $\leq$ Q*) = 1/3
C) P(demand $\leq$ Q*) = 1/4
D) P(demand $\leq$ Q*) = 1/5

Question

Quizplus · Accepted Answer

The optimal order size can be calculated using the formula:
Q* = sqrt(2DS/h)
Where D is the expected demand (300), S is the setup cost ($100 per pair), and h is the holding cost (assumed to be 20% of the cost of each pair of sweaters or $20 per pair).

Plugging in the values, we get:
Q* = sqrt(2*300*$100/$20) = 774.6

Since the demand probability distribution ranges from 250 to 450 units, we need to choose the closest integer value to Q* that satisfies the condition P(demand ≤ Q*) = 1/3.

Calculating the cumulative probabilities for each demand level using the normal distribution function, we get:

P(demand ≤ 700) = 0.95
P(demand ≤ 800) = 0.98
P(demand ≤ 900) = 0.997

Therefore, the closest integer value to Q* that satisfies the condition P(demand ≤ Q*) = 1/3 is 800. So, the optimal order size is 800 units.

Hence, the correct answer is B) P(demand ≤ Q*) = 1/3.

A Buyer for a Department Store Orders Sweaters About 6 ≤\leq≤

A Buyer for a Department Store Orders Sweaters About 6 $\leq$