SOLUTION: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number
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Question 966145: The cost C in pesos of operating a certain wood-cutting machine is related to the number of minutes n the machine is run by the function C(n) = 2.2n^2 - 66n + 655. For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2.2n^2 - 66n + 655 is a quadratic equation that opens up and points down.
the graph of that equation looks like this:
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the minimum point on the graph of that equation is found by the formula:
x = -b/2a
the quadratic formula in standard form is ax^2 + bx + c = 0
just replace n with x and your equation will conform to this convention.
2.2n^2 - 66n + 655 becomes 2.2x^2 - 66x + 655.
since this equation is in standard form, then:
a = 2.2
b = -66
c = 655
x = -b/2a becomes x = 66/4.4 which becomes x = 15
when x = 15, 2.2x^2 - 66x + 655 becomes 2.2(15)^2 - 66(15) + 655 which becomes 160.
the minimum point on the graph is when x = 15 and y = 160.
that can be seen on the same graph with y = 160 added to it as shown below:
}
the question is:
For what number of minutes is the cost of running the machine a minimum? What is the minimum cost?
the answer is:
the minimum cost is 160 pesos when the machine has been running for 15 minutes.
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