Question

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

Answer 1

the manufacturing numbers equal to the demand

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

The answer is C

Answer 2

The optimum point occurs when supply and demand are equal.

We then have to equalize both equations:

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Rewriting the equation we have:

`image`

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

`image`

The solutions of the equation are:

`image`

We discard the negative root.

We have then:

`x = 16`

Answer:

The optimum number of items to be manufactured is:

c: 16