1. If the cost function and demand curve for a certain product are C(x) = 60x + 7200 and P=300 – 2x respectively.

Find

a. The total revenue function

b. The marginal Revenue Function

c. The marginal Cost Function

d. Point(s) at which there is break even

e. The value of x at which marginal revenue equal to marginal cost

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Cost function for a certain product C(x) = 60x + 7200

Demand function p=300 – 2x

a. The total revenue function R(x)=x*p

=x(300-2x)

=-2x^2+300x

b. Marginal revenue is the derivative of the revenue function R(x).

R(x)=-2x^2+300x

R'(x)=-2*2*x+300

=-4x+300

c. Marginal cost is the derivative of the cost function C(x).

C(x) = 60x + 7200

C'(x)= 60

d. The profit function P(x) is given by R(x)-C(x)

P(x)==-2x^2+300x-60x-7200

=-2x^2+240x-7200

Break-even point is the point at which cost = revenue, i.e. Profit = 0

So, -2x^2+240x-7200=0

x^2-120x+3600=0

(x-60)^2=0

Therefore, x=60

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