SOLUTION: Suppose that the cost C, in dollars, of producing x chairs in a factory is given by the following equation: C = 2x2 – 40x + 2400 How many chairs can be produced for $4650?

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Suppose that the cost C, in dollars, of producing x chairs in a factory is given by the following equation: C = 2x2 – 40x + 2400 How many chairs can be produced for $4650?       Log On

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Question 462147: Suppose that the cost C, in dollars, of producing x chairs in a factory is given by the following equation:
C = 2x2 – 40x + 2400
How many chairs can be produced for $4650?
Your Solution





Found 2 solutions by rwm, graphmatics:
Answer by rwm(914) About Me  (Show Source):
You can put this solution on YOUR website!
4650= 2x2 – 40x + 2400

Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
Let us first replace the C in the equation C = 2x^2 – 40*x + 2400 by the amount $4650. So we get
4650 = 2*x^2 – 40*x + 2400
0 = 2*x^2 - 40*x + 2400 - 4650
0 = 2*x^2 - 40*x - 2250
Let's divide out the 2 and get
0 = x^2 - 20*x - 1125
x^2 - 20*x - 1125 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-20x%2B-1125+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-20%29%5E2-4%2A1%2A-1125=4900.

Discriminant d=4900 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+4900+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+4900+%29%29%2F2%5C1+=+45
x%5B2%5D+=+%28-%28-20%29-sqrt%28+4900+%29%29%2F2%5C1+=+-25

Quadratic expression 1x%5E2%2B-20x%2B-1125 can be factored:
1x%5E2%2B-20x%2B-1125+=+1%28x-45%29%2A%28x--25%29
Again, the answer is: 45, -25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B-1125+%29

So x = 45 is how many chairs can be produced for $4650