Question

Consider the following total revenue and total cost functions of

a firm: TR=150q−3q2 and TC=−24q2+143q−200, where q is the number of
units produced and sold. Determine the firm's profit when q=20.

A. R8740
B. R1800
C. R6940
D. None of the given solutions is true

Answer 1

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.