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HW 2 – Business Analytics

This page provides guidelines for this homework assignment. You do not need to write anything in response to the items on this page. Questions start from the next page.

To solve the problem on the next page, you will need to 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 and a Sensitivity Report, if needed.

c. Answer the questions stated in the problem (in words).

Please submit only one file in PDF format with your write-up. Do not submit your Excel file. Your writeup must include the answer report and the sensitivity report generated by Excel Solver, whenever needed. If you make any additional assumptions, state them clearly.

Problem 1: Hyperloop

Elon Musk’s newest venture is the 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 the first class is 60 inches.  The federally mandated seat pitch for the 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 tickets of each type should be sold in order to maximize profits?

b) If Elon Musk wants to increase the total capacity of the train without changing anything else, how much should he pay for an additional unit of increase in capacity? If the capacity has been increased from 50 to 60, does Elon Musk still have incentives to further increase the capacity? Please explain.

c) 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 reduce the length of the seating area of each train by 50%. Other design elements remain unchanged. Given that Elon Musk is unwilling to increase prices, how many tickets of each type should be sold in order to maximize profits? To gain more profits under this new design, should Elon Musk argue to reduce the minimum number of first-class and coach tickets to be sold per trip, as required by the federal regulations? Please explain.