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the supply function for manufacturing a certain item is p (x)=x^2+46x-66. the demand is p (x)=56x+30. if x represents he number of items (in hundreds) what is the optimum number of items to be manufactured?

a:600
b:960
c:16
d:1600

PLEASE HURRY I'M TIMED

Respuesta :

the manufacturing numbers equal to the demand

x^2+46x-66=56x+36 then solve X

The answer is C

carlosego

The optimum point occurs when supply and demand are equal.

We then have to equalize both equations:

[tex] x ^ 2 + 46x-66 = 56x + 30
[/tex]

Rewriting the equation we have:

[tex] x ^ 2 + 46x-56x-66-30 = 0

x ^ 2-10x-96 = 0
[/tex]

From here, we solve solve the quadratic equation and clear x:

[tex] (x-16) (x + 6) = 0
[/tex]

The solutions of the equation are:

[tex] x1 = 16

x2 = -6
[/tex]

We discard the negative root.

We have then:

[tex] x = 16 [/tex]

Answer:

The optimum number of items to be manufactured is:

c: 16

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