Final answer:
The firm's profit when q=20 is found by calculating total revenue and total cost using their respective equations, then subtracting total cost from total revenue. The profit at q=20 is R9980, which means that the correct answer is D. None of the given solutions is true.
Step-by-step explanation:
To determine the firm's profit when q=20, we need to calculate the total revenue (TR) and total cost (TC), then subtract the total cost from the total revenue. The total revenue and total cost functions provided are TR = 150q - 3q2 and TC = -24q2 + 143q - 200. Substituting q=20 into these equations gives us the following:
Total Revenue:
TR = 150(20) - 3(20)2
TR = 3000 - 3(400)
TR = 3000 - 1200
TR = 1800
Total Cost:
TC = -24(20)2 + 143(20) - 200
TC = -24(400) + 2860 - 200
TC = -9600 + 2860 - 200
TC = -11040 + 2860
TC = -8180
Now, we calculate the profit by subtracting the total cost from the total revenue:
Profit = TR - TC
Profit = 1800 - (-8180)
Profit = 1800 + 8180
Profit = 9980
Therefore, the firm's profit when q=20 is R9980, which means that none of the given solutions is correct, so the answer is D. None of the given solutions is true.