Please answer this question

1. It is known that there are 3 companies in the market. Every company has the same market power. The demand function in the market is D(P): Q = 4000 4P. It should be noted that the quantity of goods supplied in the market (Q) is the sum of the quantities of each firm or Q = q1 + q2 + q3. Even though they have the same power, but the three companies have different total costs, the total costs of each company are as follows:

Where: TC1 =100+4q²1 +10q1; TC2 =150+4q²2 +8q2; TC3 = 100+3q²3 +10q3. Question: a. Find the profit equation for each company. b. Calculate the total output (= production) of each firm at the time the maximum profit is reached. Use solving through matrices. c. What is the equilibrium price and quantity in the market when each firm maximizes the advantage? d. What is the profit of each company? e. Explain what causes the difference in profits. Use comparative static analysis