Suppose a firm's variable cost function is given by the following relationship, where Q represents the firm's output (Q = output):

VC = 200Q - 9Q2 + 0.25Q3

The firm's fixed costs are estimated as $150.

a. State the total cost function (TC).

b. Determine the functions for

(i) average fixed cost (AFC),

(ii) average variable cost (AVC),

(iii) average total cost (ATC),

(iv) marginal cost (MC)

c. Determine the value of Q where the average variable cost function takes on its minimum value. Hint: Take the first derivative of the AVC function, set the derivative equal to 0, and solve for Q. Also use the second derivative to check for a maximum or minimum.

d. Determine the value of Q where the marginal cost function takes on its minimum value.

e. Plot the AVC and MC functions on a single graph for the values of Q = 2, 4, 6... and 24

f. Referring to the cost functions graphed above, determine the value that minimises AVC and MC.

g. Compare answers in f with those in c and d.