Question

The Electric Company owns three power generators, each of which is painted a different color. During any hour, the red generator can produce up to 500 kilowatt hours (kWh) at a cost of $1.00/kWh in raw materials. The blue generator can produce up to 200 kWh at a cost of $3.00/kWh in raw materials. The green generator can produce up to 100 kWh at a cost of $2.00/kWh in raw materials. Regardless of how much electricity is produced, the firm must pay its $100 to its workers according to a union contract. The machines are worth $100,000; if the firm did not own these machines, the money invested in the machines would be invested in bonds yielding 68¢ an hour.

a. If electricity sold for $2.25/kWh, how much electricity would the Electric Company produce? (Hint: Think about which generator(s) it would make sense to run.)
b. What would total revenues, total costs, and total profits be?

Answer 1

If electricity sold for $2.25/kWh, the Electric Company would produce 600 kWh, with a revenue of $1,350, total costs of $800.68, and a profit of $549.32 using the red and green generators.

Step-by-step explanation:

When determining how much electricity the Electric Company would produce if electricity sold for $2.25/kWh, it is essential to consider the cost of producing this electricity with each generator. For the red generator, the cost is $1.00/kWh, for the blue generator it is $3.00/kWh, and for the green generator, it is $2.00/kWh. Since the selling price is $2.25/kWh, only the red and green generators would be used because the cost of production with the blue generator would result in a loss.

The red generator can produce up to 500 kWh, and the green can produce up to 100 kWh. Producing these amounts would result in revenues of $1,350 (600 kWh * $2.25/kWh). The costs would include the raw material costs of $500 for the red generator (500 kWh * $1.00/kWh) and $200 for the green generator (100 kWh * $2.00/kWh), as well as the fixed labor costs of $100, totaling $800. An additional cost of $0.68 must be considered for the opportunity cost of the bonds that could have been issued instead of purchasing the generators. Therefore, the total costs would be $800.68.

The total profits would then be calculated by subtracting the total costs from the total revenues, resulting in a profit of $549.32 ($1,350 - $800.68). This scenario assumes the maximum output for both generators within the profitable range.