What price should it charge if it wants to maximize its revenue in the short-run?

Problem 7 on page 342 of the textbook: The demand and cost function for a company are estimated to be as follows:

P= 100 8Q

TC = 50 + 80Q -10Q2 + 0.6Q3

a. What price should the company charge if it wants to maximize its profit in the short-run?
b. What price should it charge if it wants to maximize its revenue in the short-run?
c. Suppose the company lacks confidence in the accuracy of cost estimated expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit maximizing and revenue maximizing prices?

problem 2
You are given the following cost functions:

TC = 100 + 60Q – 3Q2 + 0.1Q3

TC = 100 + 60Q + 3Q2

TC = 100 + 60Q

a. Compute the average variable cost, average cost, and marginal cost for each function.
Plot them on a graph
Using Table 7.2 Chapter 7, page 255 as a reference

b. In each case, indicate the point at which diminishing returns occur. Also indicate the point of maximum cost efficiency (i.e., the point of minimum average cost).

c. For each function, discuss the relationship between marginal cost and average variable cost and between marginal cost and average cost. Also discuss the relationship between average variable cost and average cost.