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6. The total profit made by an engineering firm is given by the formula p = x2 – 25x + 5000. Find the minimum profit made by the company.

Guest Feb 6, 2015

Best Answer 

 #1
avatar+17705 
+13

When graphed, the equation  p = x² - 25x + 5000  is a parabola, rising from the vertex.

Since it has a minimum point and opens upward, the problem is to find the vertex (which is the location of the minimum point).

This can be done in several ways: one way is to graph it, another is to use a formula, and a third is to "complete the square".

The following explains how to complete the square:

First, move the constant term to the other side:

--->   p - 5000  =  x² - 25x

Second, divide the coefficeint of the linear term by 2, and square the result:

--->   -25 ÷ 2  =  -12.5

--->   (-12.5)² =  156.25

Third, add this value to both sides:

--->   p - 5000 + 156.25  = x² - 25x + 156.25

Fourth, simplify the left side and factor the right side:

--->   p - 4843.75  =  (x - 12.5)²

Fifth, determine the vertex:

--->   x = 12.5, y = 4843.75

The minimum value is the y-value:  4843.75

geno3141  Feb 7, 2015
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2+0 Answers

 #1
avatar+17705 
+13
Best Answer

When graphed, the equation  p = x² - 25x + 5000  is a parabola, rising from the vertex.

Since it has a minimum point and opens upward, the problem is to find the vertex (which is the location of the minimum point).

This can be done in several ways: one way is to graph it, another is to use a formula, and a third is to "complete the square".

The following explains how to complete the square:

First, move the constant term to the other side:

--->   p - 5000  =  x² - 25x

Second, divide the coefficeint of the linear term by 2, and square the result:

--->   -25 ÷ 2  =  -12.5

--->   (-12.5)² =  156.25

Third, add this value to both sides:

--->   p - 5000 + 156.25  = x² - 25x + 156.25

Fourth, simplify the left side and factor the right side:

--->   p - 4843.75  =  (x - 12.5)²

Fifth, determine the vertex:

--->   x = 12.5, y = 4843.75

The minimum value is the y-value:  4843.75

geno3141  Feb 7, 2015
 #2
avatar+3682 
+5

nice, geno!!!! woop woop

BrittanyJ  Feb 7, 2015

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