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

#1**+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

#1**+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