Question

If the cost, C(x), for manufacturing x units of a certain product is given by C(x)=x^2-14x+74, find the number of units manufactured at a cost of $9050

Answer 1

Steps:

So for this, since C(x) is the cost, and we are given the cost of $9050, we will plug 9050 into C(x) and solve for x:

$9050=x^2-14x+74$

So for this, I will be completing the square. Firstly, subtract 74 on both sides of the equation:

$8976=x^2-14x$

Next, we want to make the right side of the equation a perfect square. To find the constant of this soon-to-be perfect square, you need to divide the x coefficient by 2, square the quotient, then add the result on both sides of the equation. In this case:

-14 ÷ 2 = -7, (-7)² = 49

$9025=x^2-14x+49$

Next, factor the left side:

$9025=(x-7)^2$

Next, square root both sides:

$\pm\ 95=x-7$

Next, add 7 to both sides:

$7\pm 95=x$

Next, solve the left side twice. Once with the plus symbol, once with the minus symbol:

$102,-88=x$

Answer:

Since we cannot have negative units in this context, at the cost of $9050 you can manufacture 102 units.