Question

If the cost, C(x), for manufacturing x units of a certain product is given by

Answer 1

Answer:

99 units.

Step-by-step explanation:

The cost function for manufacturing x units of a certain product is:

$C(x)=x^2-15x+34$

We want to find the number of units manufactured at a cost of $8350. Therefore:

$8350=x^2-15x+34$

Subtract 8350 from both sides:

$x^2-15x-8316=0$

This equation can be a bit difficult to factor, if even possible, so we can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 1, b = -15, and c = -8316. Thus:

$\displaystyle x=\frac{-(-15)\pm\sqrt{(-15)^2-4(1)(-8316)}}{2(1)}$

Simplify:

$\displaystyle x=\frac{15\pm\sqrt{33489}}{2}$

Evaluate:

$\displaystyle x=\frac{15\pm183}{2}$

Therefore, our solutions are:

$\displaystyle x=\frac{15+183}{2}=99\text{ and } x=\frac{15-183}{2}=-84$

We cannot produce negative items, so we can ignore the second answer.

Therefore, for a cost of $8350, 99 items are being produced.