Answer:
Fashionables should order 625 units of sweaters to maximize its expected profit.
Step-by-step 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.