A firm’s cost function and the demand functions are

*C *( *x *) = 5*x *and *p *= 25 - 2*x *respectively, where *x *is the amount produced and/or demanded.

(a) Find the output level that will maximize the firm’s profits. What is the

maximum profit?

(b) If a tax of *t *per unit is imposed, which the firm adds to its cost, find the output level that will maximize the firm’s profits. What is the maximum profit? (Note that the optimal output and profits will both be functions of the tax rate *t *rather than some fixed values.)

(c) Determine the tax *t *per unit that must be imposed to obtain the maximum tax revenue. (Hint: Use the solution of output as a function of *t *from 2(b) to formulate the tax revenue function.)

(d) Given the solution for *t *in (c), find the optimal output and profits using their optimal choice functions in (b). (This time, the solutions will be some fixed values.)

I have absolutely no clue how to do these - could someone show me how to do these please?