Question 47941
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.