Answer to Question #187535 in Math for kris

Question

4.The profit function and the average cost function for a product of a company are

p(x) = - 4000 + 194x - 0.149x² in ringgit and ________ 4000

C(x) = 6 - 0.001x + ^________

^x

ringgit respectively, when x is the quantity sold in units. Find

(a) the total cost function

(b) the revenue function

(c) the quantity which will maximize the profit

(d) the maximum profit

(e) the price at maximum profit

Answer 1

(a) The total cost function is:

$C(x) = 6x - 0.001x^2 + 4000.$

(b) The revenue function is:

$R(x) = p(x) + C(x) = -4000 + 194x - 0.149x^2 + 6x - 0.001x^2 + 4000 = -0.15x^2 + 200x.$

(c) The quantity which will maximize the profit is:

p'(x) = 194 - 0.298x = 0,

x = 194/0.298 = 651 units.

(d) The maximum profit is:

$p(x) = -4000 + 194×651 - 0.149×651^2 = 59,147.65.$

(e) The price at maximum profit is:

p = R(x)/x = -0.15×651 + 200 = 102.35.