Maximizing Profit in Coat Manufacturing Industry
What factors should a coat manufacturer consider when deciding between building a large factory or a small factory?
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.
| Event 1 | Event 2 | Event 3 | Event 4 | |
|---|---|---|---|---|
| Action A | $160,000 | $400,000 | $520,000 | $1,240,000 |
| Action B | -$90,000 | $150,000 | $270,000 | $990,000 |
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.
| Event 1 | Event 2 | Event 3 | Event 4 | |
|---|---|---|---|---|
| Action A | $0 | $0 | $0 | $0 |
| Action B | $250,000 | $250,000 | $250,000 | $250,000 |
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.