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1.      If the cost function and demand curve for a certain product are C(x) = 60x...

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davene25 | Student, Undergraduate | (Level 1) eNoter

Posted October 14, 2013 at 5:51 PM via web

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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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llltkl | College Teacher | (Level 3) Valedictorian

Posted October 14, 2013 at 6:58 PM (Answer #1)

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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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