# the cost function and demand curve for a certain product are c(x)=60x+7200 and p=300-2x find the total revenue function the marginal revenue function the marginal cost function point at which there...

the cost function and demand curve for a certain product are c(x)=60x+7200 and p=300-2x find

the total revenue function

the marginal revenue function

the marginal cost function

point at which there is breakeven

the value of x at which marginal revenue equal to mrarginal cost.

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Given the cost function for a certain product C(x) = 60x + 7200

Demand function p=300 – 2x

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

=x(300-2x)

**=-2x^2+300x**

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

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

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

**=-4x+300**

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

C(x) = 60x + 7200

**C'(x)= 60**

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

or, x^2-120x+3600=0

or, (x-60)^2=0

Therefore, x=60

Next, plug-in the value of x to either cost or revenue function.

C(x)=60x+7200

or, C(60)=60*60+7200=10800

**Hence, the break even point is (60,10800).**

To find the value of x at which marginal revenue equal to marginal cost set:

R'(x)=C'(x)

or, 300-4x=60

or, x=60

**Therefore, at x=60, marginal revenue is equal to marginal cost.**

**Sources:**