if the cost, C, for manufacturing x units of a certain product is given by C=x^2-10x+50, find the number of units manufactured at a cost of $9050.

Question

 There are __________ units manufactured at a cost of $9050.

Answer 1

C = 9050, so replace C to start with:

 

9050 = x² - 10x + 50

 

Now time to solve for x:

 

0 = x² - 10x - 9000

 

Solve by factoring or quadratic formula, I'll show factoring:

 

0 = (x - 100)(x + 90) 

 

So we get x = 100 or x = -90. 

 

Only 100 makes sense, so there are 100 units manufactured. 

 

You can check this by 100² - 10(100) + 50 = 9050