if the cost cx for manufacturing x units of a certian produc

if the cost c(x) for manufacturing x units of a certian product is given by the equation c(x) =x^2+3x+100, find the number of units manufactured at a cost of $280.

Solution

C(x) = x^2 + 3x + 100

C(x) = $ 280

280 = x^2 +3x +100

x^2 +3x - 180 =0

x^2 +15x -12x - 180 =0

x(x+15) -12(x + 15) =0

(x-12)(x+15) =0

x= 12, -15 .Neglect x=-15 as no. of units cannot be -ve

So, 12 units are manufactured at a cost of $ 280