Question

The cost C(x) for manufacturing x units of a product is given by the formula C(x) = x2 - 60x + 4000. Find the number of units manufactured at a cost of $6700.

Answer 1

Answer:

$x=90$

Step-by-step explanation:

The first step is to substitute $6700 in the position of C(X) in the formula:

$C(x)=x^2-60x+4000\\6700=x^2-60x+4000\\x^2-60x-2700=0$

To solve the second-degree equation use the formula:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Where $a$ is the coefficient of the$x^2$ ($a=1$), $b$ is the coefficient of the $x$ ($b=-60$) and $c$ is the constant part ($c=-2700$)

$x_{1,2}=\frac{60\pm\sqrt{(-60)^2-4(1)(-2700)} }{2(1)}\\x_{1,2}=\frac{60\pm\sqrt{3600+10800} }{2}\\x_{1,2}=\frac{60\pm\sqrt{14400} }{2}\\x_{1,2}=\frac{-60\pm120 }{2}$

$x_{1}=\frac{60+120 }{2}=90$

$x_{2}=\frac{60-120 }{2}=-30$

The number of units manufactures is 90. The other value of x doesn't make sense in the contest of the problem.