SOLUTION: Hi, please help me answer this question: The president of a company producing water pumps has gathered data suggesting that the average cost in dollars producing x units per hou

Question 107033: Hi, please help me answer this question:
The president of a company producing water pumps has gathered data suggesting that the average cost in dollars producing x units per hour of a new style of pump will be C(x)=x^2-22x+166. Determine the number of pumps per hour to produce to keep the average cost below $75 per pump.
Thanks!
Found 2 solutions by Annabelle1, edjones:
Answer by Annabelle1(69) (Show Source): You can put this solution on YOUR website!
you need to solve C(x)=x^2-22x+166<75
s0 x^2-22x+166-75<0
x^2-22x+91<0
this isn't factorisable so put it into the quadratic formula
a=1 b=-22 c=91

x=(22+-sqrt(120)/2
x=16.477
or
x=5.523

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!

Between 6 and 16 pumps per hour should do the trick according to my graphing calculator and the graph above. At 11 pumps/h the cost reaches a minimum of about $45.
.
if you want to do the math:
x^2-22x+166<=75
x^2-22x+91<=0
5.52...<=x<=16.48...
Ed

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=120 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 16.4772255750517, 5.52277442494834. Here's your graph:

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