Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = - 2x^2 + 8x + 2, where x is the number of units produced per week, in thousands.

a. How many units should the company produce per week to earn the maximum profit?

b. Find the maximum weekly profit

Question

Mathematics

Wally

17 July, 03:17

Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = - 2x^2 + 8x + 2, where x is the number of units produced per week, in thousands.

a. How many units should the company produce per week to earn the maximum profit?

b. Find the maximum weekly profit

+3

Answers (1)

Know the Answer?

Avah Obrien · Answer 1

P = - 2x^2 + 8x + 2

for maximum P, dP/dx = 0

dP/dx = - 4x + 8 = 0

4x = 8

x = 2

The company should produce 2,000 units per week to earn maximum profit.

Maximum profit = - 2 (2) ^2 + 8 (2) + 2 = - 8 + 16 + 2 = 10

Therefore, the maximum weekly profit is $1,000.