Question

If the cost. C, for manufacturing x units of a certain product is given by C= x² + 10x +30, find the number of units manufactured at a cost of $11,030.

Answer 1

The number of units manufactured at a cost of $11,030 was 100.

Explanation:

I graphed the function on the graph below and found the point where C = 11,030. When C = 11,030, x is 100

Answer 2

100 units

Explanation:

We want to find x when ...

C = 11030

x² +10x +30 = 11030 . . . . fill in for C

x² +10x = 11000 . . . . . . . . subtract 30

x² +10x +25 = 11025 . . . . add 25 to complete the square

(x +5)² = 105² . . . . . write as squares

x +5 = ±105 . . . . . . . take the square root

x = -5 ±105 = {-110, 100}

The number of units manufactured at a cost of $11,030 is 100.