The demand and cost function for a company are estimated to be as follows: P = 100 - 8Q TC = 50+80Q-10Q^2 +0.6Q^3 a. what price should the company

Please help..

The demand and cost function for a company are estimated to be as follows:

P = 100 - 8Q

TC = 50+80Q-10Q^2 +0.6Q^3

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 estimates 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?

Actually, I have the solutions, but I do not understand how they reached this conclusion "

There will be no significant difference, the revenue maximizing price would remain the same but the profit maximizing price increases to $90" can you please show me teh calculations?

I am attaching the solution

Thank you