Problem 2: Modeling and Linear Optimization

The Pembrook Inn has 200 identical rooms, which are booked at three different rates ($79, $99 and $129), via three distinct marketing channels. The manager has provided you with the demand forecast in Table 1, by rate and length of stay, for five days in November. The numbers in Table 1 represent unique requests in each day - for instance, for this particular Monday in November, roughly 45 customers request a one-night stay in a $79 room, an additional 36 (different) customers request a 2-night stay for $79ight rate, another 9 customers request a 3-night stay at $79ight, etc. Ultimately, the manager would like to maximize the revenue he gets from guests staying in the hotel, given the expected requests for rooms that the hotels will receive.

Remark. For the purposes of this model, you may (a) ignore any integrality considerations (i.e., feel free to make fractional room allocations), (b) ignore any capacity considerations during the days following Friday (e.g., assume that any 2-day stay reservation made on Friday can be honored on Saturday), and (c) consider the full revenue resulting from the bookings you make. If you feel that the case or one of the questions is ambiguous, state clearly any additional assumptions that you need to make, and proceed with the analysis accordingly.

Length of Stay (nights) 1 12 3 12 3 12 13 Room Rate (per night) $79 $79 $79 $99 $99 $99 $129 $129 $129 Monday 45 36 9 20 16 4 15 12 3 Tuesday 72 24 24 42 14 14 24 8 8 Wednesday 77 22 21 56 16 8 42 12 6 Thursday 72 8 0 54 6 27 3 Friday 50 40 10 15 12 3 5 4