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

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25 January, 00:45

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

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Answers (1)

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Angelina Mooney · 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.