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

`x=90`

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)=(-b\pm√(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)=(60\pm√((-60)^2-4(1)(-2700)) )/(2(1))\\x_(1,2)=(60\pm√(3600+10800) )/(2)\\x_(1,2)=(60\pm√(14400) )/(2)\\x_(1,2)=(-60\pm120 )/(2)`

`x_(1)=(60+120 )/(2)=90`

`x_(2)=(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.