Compute the value of the Lagrange multiplier

Compute the value of the Lagrange multiplier

You are organizing a rock concert to benefit Amnesty International. The concert is to be held in a football stadium that has a seating capacity of 56,000. There are two kinds of seating: reserved and general. Demand for these seats is estimated as:

PR = 100-.00125 QR and PG = 60-.00125 QG

Where PR and PG denote ticket prices for reserved and general seating and QR and QG are the number of those seats

All artists and support staff are donating their time however there is a fixed cost of $100,000.

a) Using the method of the Lagrange multiplier compute the prices that you will charge to so that the profit is maximized and at the same time the stadium will be filled to capacity.

Compute the number of each type of tickets sold, as well as the consequent profit level.

b) Compute the value of the Lagrange multiplier. Describe its economic significance in this case.