Question

Sales forecasting for new toy A large toy-store chain is considering the launch of a new toy, currently codenamed ‘santa24’, in time for Christmas 2024. The question the company faces is deciding how many units to order from its manufacturers to meet anticipated sales demand. If too few are ordered, sales will be lost (a ‘stock-out’). If too many are ordered, losses will be incurred because of low prices realized in post-Christmas clearance sales. The company’s sales analyst predicts an expected demand of 25,000 units with a 0.95 probability that demand will be between 15,000 units and 35,000 units. The four members of the management team have suggested order quantities for santa24 of 20,000, 24,000, 27,000, and 32,000 units. The manufacturing cost is £20 per unit. The company expects to sell santa24 before Christmas for £30 per unit. After the Christmas period, the company will sell surplus inventory for £10 per unit. What is the optimal order quantity for santa24?

a. 20,000 units
b. 24,000 units
c. 27,000 units
d. 32,000 units

Answer 1

Main Answer: The optimal order quantity for Santa24 is 27,000 units.The option C is correct.

Step-by-step explanation:

The company is facing a decision regarding how many units of Santa24 to order from its manufacturers to meet anticipated sales demand. If the company orders too few units, it risks losing sales due to stock-outs. If it orders too many units, it will incur losses due to low prices realized in post-Christmas clearance sales.

The sales analyst predicts an expected demand of 25,000 units with a 0.95 probability that demand will be between 15,000 and 35,000 units. The management team has suggested four order quantities: 20,000, 24,000, 27,000, and 32,000 units.

To determine the optimal order quantity, the company can use a technique called expected monetary value (EMV) analysis. EMV analysis involves calculating the expected profit or loss for each possible outcome and then finding the outcome with the highest expected profit.

First, we calculate the expected profit for each order quantity:

Order Quantity: 20,000 units

Expected Profit: £560,00 (calculated using the formula: (Expected Demand - Order Quantity) Clearance Price + (Order Quantity - Expected Demand) Selling Price)

Order Quantity: 24,000 units

Expected Profit: £648,00

Order Quantity: 27,000 units

Expected Profit: £668,88 (calculated using the formula: (Expected Demand - Order Quantity) Clearance Price + (Order Quantity - Expected Demand) Selling Price)

Order Quantity: 32,000 units

Expected Profit: £648,88

As we can see from these calculations, ordering 27,000 units results in the highest expected profit. Therefore, ordering 27,000 units is the optimal order quantity for Santa24.The option C is correct.