Homework Answers
TC = 72-6t ; TR = 144 - t2 (I am assuming that its a square and not multiplied by 2 because 2 is placed after t in the question you have provided to me).
a. Since the sales manager's goal is to maximise revenue, and since t enters with a minus, she should minimise t to maximise revenue. Therefore, the minimum possible t is t = 0. Any higher t would result in lesser TR.
b. In order to minimise TC, the production manager will have to maximise t since it enters after a minus sign. A higher t means lower TC, until TC = 0. Therefore, solve for 0 = 72-6t. t = 12
c. In order to maximise profit, we could either maximise (TR - TC) by differentiating it with respect to t and equating it to 0, or we could simply use the microeconomic identity: MR = MC to maximise profits. (It is the same thing)
So, MR = -2t. MC = -6. Therefore, t = 3.
d. When CEO believes that the TC is 72 - 12t, solve it similar to part (c), and you will get t = 6.
e. Calculate profits from both parts c and d and subtract the higher one from the lower one to get the loss due to wrong information regarding costs. I think you can manage this.
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