Final answer:
The equations to find the values of P1, P2, Q1, and Q2 that maximize profits is Q1 = 140 - 2P1, Q2 = 100 - 2P2, and Q1 + Q2 = 32.
Step-by-step explanation:
Individual Demand Curves:
For on-campus (residence) students: Q1 = 140 - 2P1
For off-campus students: Q2 = 100 - 2P2
Total Quantity Constraint:
Due to the capacity constraint of the luxury box, Q1 + Q2 = 32
Total Cost Function:
Total costs are given by C = 0.5Q2
Profit Maximization:
To maximize profits, the union needs to set prices P1 and P2 such that they maximize the profit function.
Additional Constraint:
Prices will be set based on the third-degree price discrimination plan, meaning different prices for different groups.
The profit function (π) is given by the revenue (R) minus the cost (C):
π = R - C
π = (P1 * Q1 + P2 * Q2) - 0.5Q2
The constraints are Q1 = 140 - 2P1, Q2 = 100 - 2P2, and Q1 + Q2 = 32.
You can use these equations to find the values of P1, P2, Q1, and Q2 that maximize profits. This involves solving the system of equations formed by the demand and constraint equations. This will help determine the optimal pricing and quantities to maximize profit given the capacity and demand constraints.
Your full question was
UTMSU has rented a luxury box at Roger’s Centre for a Raptors versus Cleveland game. Residence students have demand given by Q1 = 140 − 2P1 and students who live off-campus have demand Q2 = 100 − 2P2. Total costs are given by C = 0.5Q2. Organizers discover that the luxury box will only hold 32 persons. While the union is still able to pricediscriminate, they face a constraint that Q1 + Q2 = 32. write the equations to find the values of P1, P2, Q1, and Q2 that maximize profits.