Question

Question 2 [20 marks] = Given that the price of the product is P(Q) 4000 – 33Q and the Marginal Cost function of producing the same product is C' = 602 – 6Q + 400. Assuming Q> 0. a) Find the revenue and marginal revenue function of the production in term of Q. (3 Marks) b) Find the total cost function if the fixed cost of the production is RM5000. (4 Marks) c) Interpret the result of the marginal profit of the production when Q=10. (5 Marks) d) Is the profit of the production being relatively maximum or minimum (show the evidence by using second derivative test) and interpret the results? (5 marks) e) What is the profit value? (3 Marks)

Answer 1

(a)

TR = P x Q = 4000Q - 33Q²

MR = dTR/dQ = 4000 - 66Q

(b)

Since MC = dTC/dQ = 6Q² - 6Q + 400,

TC = 6 x (Q³ / 3) - 6 x (Q² / 2) + 400Q] + C, where C = TFC = 5000

TC = 2Q³ - 3Q² + 400Q + 5000

(c)

Profit (Z) = TR - TC = 4000Q - 33Q² - 2Q³ - 3Q² + 400Q + 5000 = 4400Q - 36Q² - 2Q³ + 5000

When Q = 10,

Marginal profit = dZ/dQ = 4400 - 72Q - 6Q² = 4400 - (72 x 10) - (6 x 10 x 10) = 4400 - 720 - 600 = 3080

It means that when Q = 10, marginal revenue is higher than marginal cost by RM3080.

(d)

When Q = 10,

d2Z/dQ² = - 72 - 12Q = - 72 - 120 = - 192 < 0

Therefore, profit is at a maximum.

(e)

When Q = 10,

Profit (Z) = 4400 x 10 - 36 x 100 - 2 x 1000 + 5000 = 44000 - 3600 - 2000 + 5000 = RM 43400