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?

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) (Show Source): You can put this solution on YOUR website!
4650= 2x2 � 40x + 2400
Answer by graphmatics(170) (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 (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=4900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 45, -25. Here's your graph:

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

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