A company operates two plants which manufacture the same item and whose total cost functions are c_1 = 10 + 0.01 q_1^2 \quad\mbox{and}\quad c_2 = 5 + 0.02 q_2^2, where q_1 and q_2 are the quantities p

A company operates two plants which manufacture the same item and whose total cost functions are c_1 = 10 + 0.01 q_1^2 \quad\mbox{and}\quad c_2 = 5 + 0.02 q_2^2, where q_1 and q_2 are the quantities produced by each plant. the total quantity demanded, q = q_1 + q_2 , is related to the price, p , by p = 30 - 0.02 q. how much should each plant produce in order to maximize the company's profit?