SOLUTION: The revenue and cost equations for a product are R = x(75-0.0005x) and C = 30x + 250000 Where R and C are measured in dollars and x represents the number of units sold. How many u

Algebra ->  Finance -> SOLUTION: The revenue and cost equations for a product are R = x(75-0.0005x) and C = 30x + 250000 Where R and C are measured in dollars and x represents the number of units sold. How many u      Log On


   

Question 1188436: The revenue and cost equations for a product are R = x(75-0.0005x) and C = 30x + 250000
Where R and C are measured in dollars and x represents the number of units sold. How many units must be sold to obtain a profit of at least $750000?
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The profit is revenue minus cost, so the profit is x%2875-0.0005x%29-30x-250000=-0.0005x%5E2-45x-250000.
Since we want this to equal $750,000, we get
-0.0005x%5E2%2B45x-250000=750000
-0.0005x%5E2%2B45x-1000000=0
Dividing both sides by -0.0005, we get
x%5E2-90000x%2B2000000000.
Factoring, we have %28x-40000%29%28x-50000%29=0.
Therefore, the solution is to sell either 40,000 or 50,000 units.