Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:

Question

Find the number of units that must be produced and sold in order to yield the maximum profit, given the following equations for revenue and cost:

R(x) = 60x - 0.5x²

C(x) = 10x + 8.

MULTIPLE CHOICE

70 units

50 units

51 units

58 units

Answer 1

First write an equation for profit,

As you know, profit = revenue - cost so:

P(x) = (60x - 0.5x²) - (10x + 8)

P(x) = 60x - 0.5x² - 10x - 8

P(x) = -0.5x² + 50x - 8

To maximize the function, take the derivative and set it equal to zero and solve:

P'(x) = -1x + 50

-x + 50 = 0

x = 50