. find the minimum number of units that can be produced and sold to avoid loss

Question

R=400+25x- x², C=50+50x.

Answer 1

R-c > 0

400 + 25x - x^2 - 50 - 50x > 0

350 -25x - x^2 > 0

x^2 + 25x - 350 < 0

( x + 35 )( x - 10 ) < 0

x+35 ---> -35 is a zero

x-10 ---> 10 is a zero

for x<-35 the inequality is positive , so no, not in the solution

-35 < x < 10, the inequality is negative, so yes, is part of the solution

x>10, the inequality is positive so no, not in the solution.

the solution is 0 < x < 10

Note that when x=10, the revenue is 400 + 250 - 100 = 550 and so is the cost 550 = 50 +500

1 unit will return a profit of 424 - 100 = 324