Question

Suppose that for a certain company, C(x) = 35x + 2500 represents the total cost function, and R(x) = 60xrepresents the total revenue function.(a) Find the total-profit function(b) Find the break-even point.(a) The total-profit function is P(x) =(Type your answer in slope-intercept form.)

Answer 1

Total cost function is C(x) = 35x + 2500

Total revenue function is R(x) = 60x

a)

Recall,

total profit = total revenue - total cost

Total profit function would be

P(x) = R(x) - C(x)

P(x) = 60x - (35x + 2500)

P(x) = 60x - 35x - 2500

P(x) = 25x - 2500

b) The break even point is the point where revenue - cost = 0

Revenue = cost

60x = 35x + 2500

60x - 35x = 2500

25x = 2500

x = 2500/25

x = 100

The break even occurs when x = 100