Mathematics: 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: 600b: 960c: 16d: 1600 hurry i m timed

The supply function for manufacturing a certain item

Romo2486

13.03.2022

The optimum point occurs when supply and demand are equal.

We then have to equalize both equations:

x ^ 2 + 46x-66 = 56x + 30

Rewriting the equation we have:

$x ^ 2 + 46x-56x-66-30 = 0\\x ^ 2-10x-96 = 0$

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

(x-16) (x + 6) = 0

The solutions of the equation are:

$x1 = 16\\x2 = -6$

We discard the negative root.

We have then:

x = 16

The optimum number of items to be manufactured is:

c: 16

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