SOLUTION: a manufacturer finds that the total cost C for a product is expressed by C=250x^2 - 24,000, and the total revenue R at a price of 200 per unit to be R=200x - 1,000, where x is the

Algebra ->  Graphs -> SOLUTION: a manufacturer finds that the total cost C for a product is expressed by C=250x^2 - 24,000, and the total revenue R at a price of 200 per unit to be R=200x - 1,000, where x is the       Log On


   

Question 106117: a manufacturer finds that the total cost C for a product is expressed by C=250x^2 - 24,000, and the total revenue R at a price of 200 per unit to be R=200x - 1,000, where x is the number of units sold. what is the break-even point (where total cost = total revenue) to the nearest unit?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
C=250x%5E2+-+24000
R=200x+-+1000
Find x when C=R?
C=R
250x%5E2-24000=200x-1000
250x%5E2-200x-23000=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28200+%2B-+sqrt%28+23040000+%29%29%2F%28500%29+
x+=+%28200+%2B-+%284800%29%29%2F%28500%29+
Since a negative unit sold doesn't make sense, we'll only calculate the positive value.
x+=+%285000%29%2F%28500%29+
x+=+10+
10 units is the break-even point.