The market price of an item is $250.The production cost C for the particular company is a function of its output level, q, and is given by C = 100q^(1.2), where C is in units of dollars and q is the number of units produced. The firm wants to maximize the profit, defined as total revenue minus total cost.
Determine the optimum output level to maximize the profit for the firm and derive the sufficient condition to show that the output does, in fact, represent a local maximum.
Use lagrange’s multiplier method.