If the demand is met, the total revenue is price per unit * number of units
for machine (a)
revenue = p(x)*x = 42.5x - 4x^2
cost = f(x)*x = 4.1x^2 + 92.16
breakeven is where cost = revenue
42.5x - 4x^2 = 4.1x + 92.16
4x^2 -38.4x + 92.16 = 0
x^2 - 9.6x + 23.04 = 0
x = 4.8
So, for unit (a) the breakeven occurs at 4800 units
Go forth and do likewise for (b) and (c)
a) f(x) = 4.1x +92.16
b) f(x) = 17.9x + 19.36
c) f(x) = 8.8x + 55.4
ANSWERS: a) 4.8 b) 0.93 c) 2.2, i just have no clue how they got these answers
EXTRA INFO:
The demand function for a new product is p(x)= - 4x +42.5, where x is the quantity sold in thousands and p is the price in dollars. the company that manufactures the product is planning to buy a new machine for the plant. there are 3 diff. types of machines. the cost function for each machine is shown (ABOVE). Investigate the break even quantities for each machine.
2 answers
typo: f(x) = 4.1x + 92.16, not 4.1x^2