Question

Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:

                               Rental Class

                      Super Saver Deluxe Business

Type I $30   $35        --

Room Type II $20 $30    $40

Type I rooms do not have Internet access and are not available for the Business rental class.

Round Tree’s management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms.

Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints.

Answer 1

Solution:

Let S1 denote the super saver of type I rooms, S2 denote the super saver of type II rooms, D1 denote the deluxe of type I rooms, D2 denote the deluxe of type II rooms and B2 denote the Business type II rooms.

The given data can be formulated in LPP form as follows :

MaxZ = 30S1+20S2+35D1+30D2+40B2

stc

, and

The above LPP can be solved using Excell-solver and the corresponding output is as follows:

From the output, the maximum rental value $7000 and the optimum values of decision variables is given by S1=100, S2=10, D1=0, D2=60, B2=50

The demand of Supersaver rooms is not satisfied.

The number reservations that can be accommodated in each rental class is given by

S1=100, S2=10, D1=, D2=60, B2=50

I have tried to explain it in very simple language and
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