Question

Orders for clothing from Sky manufacturer for this year's National Day’s season must be placed in June. The cost per unit for a particular dress is $10 while the anticipated selling price is $25. Demand is projected to be 25, 30, or 35 units.

There is:

• A 40 percent chance that demand will be 25 units;

• A 50 percent chance that demand will be 30 units; and

• A 10 percent chance that demand will be 35 units.

The company believes that any leftover goods will have to be scrapped.

Required:

Prepare a payoff table, and calculate how many National Day’s dresses should be ordered in June?

Answer 1

We prepare the payoff table as shown below:

The above solution in the form of formulas is shown below for better understanding and reference:

We solve the given problem by first finding Monetary value for various cases:

Case 1: Demand = 25, Purchase = 25

Case 2: Demand = 25, Purchase = 30

Case 3: Demand = 25, Purchase = 35

Case 4: Demand = 30, Purchase = 25.........and so on. We will have 9 cases for each combination of D = 25, 30, 35 and Purchase = 25, 30, 35. Accordingly, we get the monetary values.

If Demand = Purchase, Profit = Demand * Cost of Underage

If Demand is more than purchase, Profit = Purchase * Cost of Underage

If Demand is less than purchase, Profit = Demand * Cost of Underage - (Purchase - Demand) * Cost of Overage

Accordingly, based on the above table, we find Expected EMV for each option as shown below:

As seen from above, EMV is maximum for an Order quantity of 30.

Hence, 30 National Day’s dresses should be ordered in June.

The above solution in the form of formulas is shown below for better understanding and reference: