A supplier offers a seasonal product to a retailer. Demand for this product is n

Question

A supplier offers a seasonal product to a retailer. Demand for this product is normally distributed with mean 250 and standard deviation of 75. The retailer will sell the product for $90. The supplier's production cost (per unit) is $30. The supplier offers the retailer two options for purchasing: 1) The supplier sets the sales price at $75 but will credit the retailer $65 for each unsold unit. 2) The supplier sets the sales price at $55 and will not give a credit for unsold merchandise.

How much should the retailer buy if they choose option 1?

A. 269 B. 239 C. 249 D. 259

How much should the retailer buy if they choose option 2?

A. 238.83 B. 228.83 C. 218.83 D. 198.83

What is the difference in profit if they choose option 2 instead of option 1?

A. $3,148 less profits B. $4,318 more profits C. $4,318 less profits D. $3,148 more profits

Explanation / Answer

Option 1:

Underage cost Cu = Selling price - Cost = 90-75 = 15

Overage cost Co = Cost-Salvage value = 75-65 = 10

Service Probability p = Cu/(Cu + Co) = 15/(15+10) = 15/25 = 0.6

Z = 0.25 (NORMSINV(0.6) in excel)

Order quantity Q = Mean+Z*Standard deviation = 250+0.25*75 = 269

A. 269

Option 2:

Underage cost Cu = Selling price - Cost = 90-55 = 35

Overage cost Co = Cost-Salvage value = 55-0 = 55

Service Probability p = Cu/(Cu + Co) = 35/(55+35) = 0.3889

Z = -0.2822 (NORMSINV(0.3889) in excel)

Order quantity Q = Mean+Z*Standard deviation =  250+(-0.2822)*75

Q = 228.83

B. 228.83

Profit for option 1 = (90-75)*269 = 4035

Profit for option 2 = (90-55)*228.83 = 8009.05

Difference = 8009.05-4035 = 3974  more profits

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