Please show all work.Suppose that the cost of producing x units of a product can be described by the function: C(x) = 0.01x 3 - 12X 2 + 6000x +...

a)      Find the marginal cost function, MC(x).

b)     At what number of units will the marginal cost per unit be minimized? Verify that it is a minimum using the 2nd derivative test.

c)      What is the minimum marginal cost?

d)     Based upon your answer to c), explain why the total cost function is always increasing and never decreasing.

e)     Suppose that the product sells for $1500. Construct the profit function, P(x).

f)       How many units should be made to maximize profit? Verify that it is a maximum using the 2nd derivative test.

g)      What is the maximum profit? Calculate the total cost when profit is maximized (put the value of x from part f in C(x)). Calculate the average cost per unit and compare this to the price ($1500).