The total costs for a company are given by C(x) = 1500 + 50x + x^2 And the total revenues are...

Question:

The total costs for a company are given by

{eq}C(x) = 1500 + 50x + x^2 {/eq}

And the total revenues are given by

{eq}R(x) = 130x {/eq}.

Find the break-even points.

Break Even Points:

We have been given cost and revenue functions both of them polynomial in nature. To find the break even points we need to equate the cost function and the revenue function. The roots of the equations are the break even points.

Answer and Explanation:

$$C(x) = 1500 + 50x + x^2\\ R(x) = 130x $$

The breakeven points are the points at which the costs is equal to the revenue:

$$1500 + 50x + x^2=130x\\ x^2-80x+1500=0 $$

We will apply the splitting the middle term technique of factorising the quadratic equation:

$$x^2-50x-30x+1500=0\\ x(x-50)-30(x-50)=0\\ (x-50)(x-30)=0\\ x=50\\ x=30 $$


Learn more about this topic:

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How to Use the Quadratic Formula to Solve a Quadratic Equation

from Math 101: College Algebra

Chapter 4 / Lesson 10
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