A manufacturer is trying to decide whether to build Building A or Building B. The profit per unit is $5.

Building A gets an annual cost of $100,000 with a production capacity of 25,000 units each year.
Building B gets an annual cost of $200,000 with a production capacity of 50,000 units each year.
There are 4 states of nature (demand) -- 5k, 10k, 25k, & 50k units per year.
How is the payoff table constructed?

To construct the payoff table, you first need to determine the profits for each state of nature and building option.

For each state of nature (demand level), calculate the profit for each building option using the given profit per unit ($5) and the production capacity of each building.

Building A:
- For a demand of 5,000 units: Profit = Demand x Profit per unit = 5,000 x $5 = $25,000
- For a demand of 10,000 units: Profit = Demand x Profit per unit = 10,000 x $5 = $50,000
- For a demand of 25,000 units: Profit = Demand x Profit per unit = 25,000 x $5 = $125,000
- For a demand of 50,000 units: Profit = Demand x Profit per unit = 50,000 x $5 = $250,000

Building B:
- For a demand of 5,000 units: Profit = Demand x Profit per unit = 5,000 x $5 = $25,000
- For a demand of 10,000 units: Profit = Demand x Profit per unit = 10,000 x $5 = $50,000
- For a demand of 25,000 units: Profit = Demand x Profit per unit = 25,000 x $5 = $125,000
- For a demand of 50,000 units: Profit = Demand x Profit per unit = 50,000 x $5 = $250,000

Now, you can organize these profits into a table, commonly known as a payoff table, with the demand levels as the rows and the building options as the columns. Assign the profits to their corresponding cells in the table.

Payoff Table:
Building A Building B
5,000 units $25,000 $25,000
10,000 units $50,000 $50,000
25,000 units $125,000 $125,000
50,000 units $250,000 $250,000

This payoff table shows the profit for each demand level and building option, providing a clear comparison of the potential outcomes.