A company can manufacture x x hundred items for a total cost of c = 500 + 1100 x - 100 x 2 c=500+1100x-100x2. find x x if the total cost is $ 2, 300 $2,300.

We are given the equation:

c = 500 + 1100 x - 100 x^2

Solve for x given the value of c = 2300

Rearrange and substitute:

- 100 x^2 + 1100 x + 500 = 2300

Divide everything by - 100:

x^2 - 11 x - 5 = - 23

x^2 - 11 x = - 18

Completing the square:

(x - 11/2) ^2 = - 18 + (11/2) ^2

x - 11/2 = ±3.5

x = 2, 9

So x is 2 or 9