The UnLimited offers the sweaters to Fashionables at the wholesale price of $45 per sweater, and Fashionables plans to sell each sweater at the retail price of $67 per unit. The UnLimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $22 each. As a forecast for demand, Fashionables will use a normal distribution with a mean of 600 and a standard deviation of 100. How many units of sweaters should Fashionables order to maximize its expected profit?

Fashionables should order 625 units of sweaters to maximize its expected profit.

Explanation:

In order to calculate the how many units of sweaters should Fashionables order to maximize its expected profit, we would have to use the following formula:

Optimal stocking level = Mean demand + Z * Standard deviation

According to the given data we have the following to calculate that equation:

Mean demand = 600

S0tandard deviation = SQRT(Sum of variance) = 100

z=?

Hence, we would need to calculate z value by calculation the service level as follows:

Service level = Cs / (Cs + Co)

Cost of shortage(Cs) = sales price - cost price = $67 - $45 = $22

Cost of overage(Co) = Cost price - salvage value = $45 - $22 = $23

Therefore, Service level= $22/($22+$23)=0.48

The Z value that corresponds to a service level of 0.48 is = 0.253

Therefore, Optimal stocking level = 600 + (0.253 * 100) = 625

Fashionables should order 625 units of sweaters to maximize its expected profit.

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