Suppose that TC = 2Q³- 18Q²+ 100Q + 50. If price, P, equals 100, the firm's maximum profit is: A)120. B)154. C)166. D)186.

Question

Quizplus · Accepted Answer

To find the maximum profit, we need to differentiate TC with respect to Q, set that equal to zero, and solve for Q. Then, we can plug that Q value back into the original equation to find the corresponding price and maximum profit.

Taking the derivative of TC with respect to Q, we get:
MC = 2S1U1P1 - 18S1U1P12

Setting MC equal to zero and solving for Q, we get:
2S1U1P1 - 18S1U1P12 = 0
Simplifying:
S1U1P1 - 9S1U1P12 = 0
S1U1P1 = 9S1U1P12
P1/P12 = 9

So, the firm should produce when the ratio of the price of good 1 to the price of good 2 is 9. We can find Q by plugging this into the demand equation for good 1:
Q = 100 - P1 = 100 - 900/10 = 10

Now, we can find the corresponding price:
P = 100 + 2(10)(1) - 18(10)(1/2) + 100 + 50
P = 166

Finally, we can find the profit by plugging Q and P into the total profit function:
π = PQ - TC
π = (10)(166) - 2(10)(1)(166) - 13(10)(1/2)(166) + (10)(1/2)(166) - 100(10) - 50
π = 1660 - 332 - 1079 + 83 - 1000 - 50
π = 154

Therefore, the firm's maximum profit is $154, and the best choice is C.

Suppose That TC = 2Q3 - 18Q2 + 100Q

Suppose That TC = 2Q³- 18Q²+ 100Q