SOLUTION: Profitable fruitcakes. Sharon’s revenue R (in dollars) on the sale of x fruitcakes is determined by the formula R= 50x - x². Her cost C (in dollars) for producing x fruitcakes is g

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Profitable fruitcakes. Sharon’s revenue R (in dollars) on the sale of x fruitcakes is determined by the formula R= 50x - x². Her cost C (in dollars) for producing x fruitcakes is g      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 47941: Profitable fruitcakes. Sharon’s revenue R (in dollars) on the sale of x fruitcakes is determined by the formula R= 50x - x². Her cost C (in dollars) for producing x fruitcakes is given by the formula C= 2x + 40. For what values of x is Sharon’s profit positive? (Profit = revenue – cost.)


Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
revenue R (in dollars) on the sale of x fruitcakes is determined by the formula R= 50x - x². Her cost C (in dollars) for producing x fruitcakes is given by the formula C= 2x + 40. For what values of x is Sharon’s profit positive? (Profit = revenue – cost.)

Profit = R - C
Profit = (50x-x^2)-(2x+40)> 0
-x^2+48x-40>0
x^2-48x+40<0
I graphed the quadratic to see where it was below the x axis.
0.84832619...< x < 47.151674...
Since fruitcakes are counted with natural numbers you get:
1 < x < 47
Cheers,
Stan H.