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.
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
Marginal revenue is the derivative of the revenue function R(x).
Marginal cost is the derivative of the cost function C(x).
C(x) = 60x + 7200
The profit function P(x) is given by R(x)-C(x)
Break-even point is the point at which cost = revenue, i.e. Profit = 0
Next, plug-in the value of x to either cost or revenue function.
Hence, the break even point is (60,10800).
To find the value of x at which marginal revenue equal to marginal cost set:
Therefore, at x=60, marginal revenue is equal to marginal cost.