Please answer the two problems below with specic and detailed reference to the data provided. Make sure to label each answer, whether it is in a spreadsheet, word document, or photo attachment. This is an individual assignment. You may discuss it with others, but never in front of a piece of paper, board, or screen. Refrain from sharing your final answers, since it is the reasoning shown and not the correct answers which is necessary to obtain a full score. Each Roman numeral holds up to one fifth of the full score for this assignment.

Question 1: Although no-shows and late cancellations are an ever growing issue that can slash revenues from an all-booked day, few hotels actually do charge any fees for them. Instead, just like airlines, many overbook their rooms. This means that they book more rooms than they have, in the effort to reduce the number of empty rooms in the consideration that not all guests will show up. Assume that a fully booked hotel faces between 0 and 10 no-shows/late cancellations a day with uniform probability, and that there is no loss if the number of no-shows/late cancellations equals the number of overbookings. Assume also that an empty room causes a $70 loss of revenue, and an overbooked customer causes a $50 loss of goodwill. Please, (i) create a spreadsheet table that helps a hotel decide the optimal number of overbookings for the fully booked day. (ii) Confirm with simulation the same solution x ∗ . The "(0,10)" Excel formula may be of help. (iii) How should the $50 change so that x ∗ increases by two? Explain the reason for the change, and confirm it on a new spreadsheet table.

Question 2: A company has to decide whether to invest in a $2,000,000 plant or in a $1,500,000 plant. After the start of the new plant, the company will either experience a favorable market or an unfavorable market, with direct consequences for their revenue. With the more expensive plant and a favorable market, they estimate a $3,500,000 net present revenue over the planning period. If the market will not be favorable, they estimate a $1,000,000 net present total revenue. With the less expensive plant, they estimate a $2,500,000 and $800,000 net present total revenue with favorable and unfavorable markets, respectively. If the company estimates that the market will be favorable with 60% probability and unfavorable with 40% probability, (iv) advise them on which plant to invest on.

Before deciding which plant to invest on, the company could also commission a $20,000 survey from a marketing consultant that can predict with more precision the future of the market. Whether it will predict a favorable - with with 60% probability - or unfavorable - with with 60% probability - market, the consultant is known for guessing the market future right 90% of the times. In other words, the company would be paying a few dollars for a survey to give them more confidence before deciding whether or not to commit to a big dollar investment with uncertain economy. (v) Should the survey be commissioned? Why?