A company produces two goods X and Y. The profit function of the company is given as follows:
P = I00X- 2X2 - XY + 180Y – 4Y2
The company is under obligation to produce a minimum combined output of 30 units. Find the output of X and Y subject to a total of 30 units that maximize total profit by using Lagrangian multiplier methods.
Suppose a firm has its TR and TC functions estimated as follows:
TR = 300Q-3Q2
TC = 500 + 50Q + 2Q2
Find (a) profit function of the firm, (b) the quantity of output (Q) that maximizes the firm's profit.
A manufacturer in a monopolistically competitive industry produces two different brands of a product for which the demand functions are P1=56-4Q1 and P2=48-2Q2. and the joint cost function is
TC=Q12+5Q1Q2+Q22. Find the profit maximizing level of output and the price that should be charged for each brand.
A firm faces a demand law q = 50-4p where q and p are the quantity and prices of the good respectively. Find out the price at which total revenue is maximized.