Maximizing Profit in Coat Manufacturing Industry

Determining Payoffs for Small Factory Production

To determine the payoffs for the possible levels of production for a small factory, we need to calculate the profit for each level of demand and subtract the cost of production.

The profit per coat is $12. The small factory has a production capacity of 60,000 coats per year and a cost of $200,000.

For a demand of 30,000 coats per year:
Profit = ($12) x (30,000) - ($200,000) = $360,000 - $200,000 = $160,000

For a demand of 50,000 coats per year:
Profit = ($12) x (50,000) - ($200,000) = $600,000 - $200,000 = $400,000

For a demand of 60,000 coats per year:
Profit = ($12) x (60,000) - ($200,000) = $720,000 - $200,000 = $520,000

For a demand of 120,000 coats per year:
Profit = ($12) x (60,000) - ($200,000) = $1,440,000 - $200,000 = $1,240,000

The payoffs for the possible levels of production for a small factory are as follows:

• Demand of 30,000 coats per year: $160,000
• Demand of 50,000 coats per year: $400,000
• Demand of 60,000 coats per year: $520,000
• Demand of 120,000 coats per year: $1,240,000

Determining Payoffs for Large Factory Production

To determine the payoffs for the possible levels of production for a large factory, we use the same profit per coat of $12. The large factory has a production capacity of 120,000 coats per year and a cost of $450,000.

For a demand of 30,000 coats per year:
Profit = ($12) x (30,000) - ($450,000) = $360,000 - $450,000 = -$90,000 (negative value indicates a loss)

For a demand of 50,000 coats per year:
Profit = ($12) x (50,000) - ($450,000) = $600,000 - $450,000 = $150,000

For a demand of 60,000 coats per year:
Profit = ($12) x (60,000) - ($450,000) = $720,000 - $450,000 = $270,000

For a demand of 120,000 coats per year:
Profit = ($12) x (120,000) - ($450,000) = $1,440,000 - $450,000 = $990,000

The payoffs for the possible levels of production for a large factory are as follows:

• Demand of 30,000 coats per year: -$90,000
• Demand of 50,000 coats per year: $150,000
• Demand of 60,000 coats per year: $270,000
• Demand of 120,000 coats per year: $990,000

Constructing Payoff Table

Based on the results of (a) and (b), we can construct a payoff table to indicate the events and alternative courses of action.

Constructing Opportunity Loss Table

Based on the payoff table, we can construct an opportunity loss table to determine the opportunity loss for each event and action.

The opportunity loss table compares the potential losses between building a small factory (Action A) and a large factory (Action B) based on different demand scenarios. It helps in making an informed decision regarding the size of the factory to maximize profits.