The firm's profit can be given by the profit function (x) = Px - C(x) = Px - 0.5cx² - F, where P is the product price. Assume that the firm is maximizing its profits.

a. Find the firm's adaptation

b. Find an expression for the firm's profit as a function of the product price P, the parameter c and the fixed costs F.

Show the effects on optimal production and the firm's profits by

c. Product price P increases

d. Product price P and the parameter c increase with the same percentage

e. Fixed costs F increases

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a. My solution: x = p/c

b. My solution: P = (0.5p²)/c - F

c., d. and e.: How should I solve this? Should I take the profit function given and the other function from b. and plot in some numbers and see what happens? Or is it possible to solve this graphically?