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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

Respuesta :

nobillionaireNobley
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.

Answer:

x=2000 and max profit =10,000 dollars

Step-by-step explanation:

Given that Dalco Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula

[tex]P= -2x^2 + 8x + 2[/tex],

where x is the number of units produced per week, in thousands

We can use derivative test for finding the maximum profit

Let us differentiate P with respect to x two times

[tex]P' =-4x+8\\P"=-4<0\\-4x+8=0 gives x =2[/tex]

Actual units = 2000

a) 2 units should be produced per week to get maximum profit

b) Maximum profit =

[tex]P(2) = -2(2^2)+8(2)+2\\= 10[/tex]

Maximum profit actual =10000 dollars.

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