Problem: Hyperloop Your newest venture idea is a Hyperloop service between Washington DC and Baltimore. The Hyperloop trains will offer customers a choice between coach and first-class tickets. For the venture to comply with federal regulations, it must sell a minimum of 10 first-class tickets and a minimum of 10 coach tickets per trip. Currently the profit margin is $5 for each coach ticket and $8 for each first-class ticket. Due to safety reasons, the train total capacity is 50 travelers (excluding the crew). While first-class tickets are more profitable, first-class seats take up more space relative to coach seats. The overall length of the seating area of the train is 2400 inches. The seat pitch for first class is 60 inches. The federally mandated seat pitch for coach class is 30 inches. Another consideration for deciding on the allocation of the seats is the weight capacity of the train. The allowed total passenger payload is 10000 lbs. It is also known that first-class customers are, on average, heavier than coach customers. The typical weight of a first-class customer is 200lbs, while the typical weight of a coach customer is 150lbs.

a) How many of each ticket should be sold in order to maximize profits?

b) How much would Hyperloop earn over a 10-year horizon with 365-day service, and 100 trains per day, assuming full utilization and assuming that you implement your solution in part a)?

c) Now suppose that you could spend capital to upgrade the train in one of two ways:

Upgrade 1: Spend $4 million dollars to increase the maximum number of travelers from 50 to 55.

Upgrade 2: Spend $8 million dollars to increase the seating area of the train from 2400 inches to 2600 inches.

You have three options. 1) Invest in Upgrade 1, 2) Invest in Upgrade 2, 3) Invest in Neither. Which choice maximizes profit over the 10-year horizon? Justify your answer with the sensitivity report.

d) Ignore part c. Now suppose that due to an unprecedented outbreak of a novel infectious disease, the Hyperloop must either redesign all train cars to follow the CDC guidelines for social distancing or shut down all operations. The full redesign would cost $50 Million and reduce the available seating area, and thus the maximum seating area of each train by 50% (The maximum number of passengers is not restricted). Given that you are unwilling to increase prices, how many of each ticket should be sold in order to maximize profits? Under the assumptions in (b) is the venture still profitable?

To solve the problem do the following: a. Use the Generalized Analytics Procedure (GAP) to set up your problem as follows: i. Define your model in words 1. Identify the objective function in words 2. Identify the random variables in words (none in this HW) 3. Identify the decision variables in words 4. Identify the constraints in words ii. Formulate your model mathematically 1. Define the random variables (none in this HW) 2. Define the decision variables 3. Define the objective function in terms of decision variables 4. Define the constraints in terms of the decision variables. Please include any non-negativity constraints in your formulation b. Set up the problem in Excel and use Solver to find the optimal values of the decision variables. Ask Solver to create an Answer Report. c. Answer the questions stated in the problem (in words).