This document contains information to calculate the marginal cost, marginal revenue, profit function, and profit maximizing output for a company. It provides the total revenue, total cost, and marginal cost functions. It then shows the calculations to derive the marginal revenue, profit, and profit maximizing output functions. The profit maximizing output is found to be 20 units with a maximum total profit of $15,850.

1. Example
• TR = 1400Q – 7.5Q2
• TC = Q3 – 6Q2+140Q+750
• Find out the following
• MC function
• MR function
• Profit function
• Profit Maximization out put
• Total profit

2.  MC = 3Q2 – 12Q+140
 MR = 1400-15Q
 Profit Function = 1400Q-7.5Q2 –(Q3-6Q2+140Q+750)
=-Q3-1.5Q2 +1260Q-750
 Out put = -3Q2 -3Q+1260 =0
=-3(Q2+Q-420)=0
Q=-20 Q = 20
 Take the second derivative
 = -6Q -3
= -6*20-3 = -123<0
 Profit = -(20)3-1.5(20)2+1260(20)-750 =15850