Find the break even point value of x when cost=20x+60 and revenue= x^2 -8x

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robinmoved's profile pic

robinmoved | Middle School Teacher | (Level 1) Adjunct Educator

Posted on

Break-even value is when the cost of production equals the revenue earned. No profit is earned.

Therefore, you need to set the production cost = revenue earned. Defining the variable, x=products produced.

x^2-8x=20x+60. Solve for x. 
     -20x -20x
______________

x^2-28x=60
       -60 -60
___________
x^2-28x-60=0

Factoring the quadratic, what 2 numbers can you multiply together to get -60 and add together to get -28? Answer: +2 and -30.

 

(x-30)(x+2)=0

Using the zero product property, set each factor to 0 and solve.

x=30 and x=-2. As -2 is extraneous (can't have -2 products), the answer is x=30 products.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The break-even point is when revenue earned is equal to the cost incurred.

For the production of x, the revenue is given by x^2 - 8x and the cost is 20x + 60. Equating the two and solving for x:

x^2 - 8x = 20x + 60

=> x^2 - 28x - 60 = 0

=> x^2 - 30x + 2x - 60 = 0

=> x(x - 30) + 2(x - 30) = 0

=> (x + 2)(x - 30) = 0

=> x = -2 and x = 30

Assuming x can only take on positive values, the break-even value of x is 30

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