Question

. The total cost function for a product is ?(?) = 15? + 600, and the total revenue is R(x) = 20x, where x is the number of units produced and sold.

a) Find the marginal cost.

b) Find the marginal revenue

c) Find the profit function.

d) Find the number of units that gives the break-even point.

e) Find the marginal profit and explain what it means 9.

*please show all work*

Answer 1

C(X) = 15x + 600

marginal cost is derivative of cost function

C'(x) = 15

marginal cost = $ 15

b)

R(x) = 20x

marginal revenue is derivative of revenue function

R'(x) = 20

marginal revenue = $ 20

c)

profit = revenue - cost

= 20x - ( 15x + 600 )

profit function is P(x) = 5x - 600

d)

breakevern occurs when revenue = cost

15x + 600 = 20x

subtract 15x from both sides

600 = 5x

dividing both sides by 5

x = 120

units that gives breakeven = 120 units

e)

marginal profit is derivative of profit function

P'(X) = 5

mrginal profit = $ 5

marginal profit is the profit earned when 1 additional unit is produced and sold