The revenue and cost functions for a particular product are

The revenue and cost functions for a particular product are given below. The cost and revenue are given in millions of dollars, and x represents the number of units (in thousands).

R(x) = 65x² + 4250x

C(x) = 250x + 5200

At what production level(s), rounded to the nearest whole unit, will the company break even on this product? (Enter your answers as a comma-separated list.)

Solution

At break even , Revenue equals cost which means no profit and no loss.

R(x) =C(x)

-65x2+ 4250x= 250x+5200

65x2-4000x+5200=0. Divide by 5

13x2- 800x+ 1040=0

Upon solving this quadratic equation, we get

X= 60.209 , 1.328

Or, 60 and 1 unit will bring break even.