(a) Use linear programming to determine how many reservations to accept in each
ID: 2746867 • Letter: #
Question
(a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Rental Class with room type No of Reservations Super Saver rentals allocated to room type I Super Saver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Demand by - Select your answer -DeluxeSuper SaverBusinessItem 6 rental class was not satisfied. (b) How many reservations can be accommodated in each rental class? Rental Class No of Reservations Super Saver I Deluxe Business (c) Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? - Select your answer -YesNoItem 11 (d) With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? Type I Type II Shadow Price $ $ (a) Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be allocated to room types. Rental Class with room type No of Reservations Super Saver rentals allocated to room type I Super Saver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Demand by - Select your answer -DeluxeSuper SaverBusinessItem 6 rental class was not satisfied. (b) How many reservations can be accommodated in each rental class? Rental Class No of Reservations Super Saver I Deluxe Business (c) Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered? - Select your answer -YesNoItem 11 (d) With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? Type I Type II Shadow Price $ $Explanation / Answer
Part A
Define the Decision Variables
S1 is the # of Type 1 Super-Savor rooms
S2 is the # of Type 2 Super-Savor rooms
D1 is the # of Type 1 Deluxe rooms
D2 is the # of Type 2 Deluxe rooms
B2 is the # of Type 2 Business rooms
Objective is to maximize profit
Max S1(30) + S2(20) + D1(35) + D1(30) + B2(40)
Constraints
Only 100 Type I rooms
Only 120 Type II rooms
Less than 130 rentals for Super Savor
Less than 60 rentals for Deluxe
Less than 50 rentals for the Business
Constraint Formulas
S1 + D1<=100
S2+D2+B2<=120
S1+S2<=130
D1+D2<=60
B2<=50
Lingo Linear program
Model:
MAX=s1*30+s2*20+d1*35+d2*30+b2*40;
s1+d1<=100;
s2+d2+b2<=120;
d1+d2<=60;
s1+s2<=130;
b2<=50;
END
Lingo Results
Global optimal solution found.
Objective value: 7000.000
Total solver iterations: 4
Variable Value Reduced Cost
S1 100.0000 0.000000
S2 10.00000 0.000000
D1 0.000000 5.000000
D2 60.00000 0.000000
B2 50.00000 0.000000
Row Slack or Surplus Dual Price
1 7000.000 1.000000
2 0.000000 30.00000
3 0.000000 20.00000
4 0.000000 10.00000
5 20.00000 0.000000
6 0.000000 20.00000
Is the demand by any rental class not satisfied? Explain
Yes, the demand for Super Savor is 110 rooms verses the 130 it expects. This is expected since the other rooms are more profitable.
Part B Solution (How many reservations can be accommodated in each rental class?)
Overall results is a profit of 7000 can be obtained if 110 Super Savor, 60 Deluxe and 50 Business rooms are reserved.
Part C Solution
(Management is considering offering a free breakfast to anyone upgrading from a Super Saver reservation to Deluxe class. If the cost of the breakfast to Round Tree is $5, should this incentive be offered?)
If we assume that the profit of the Deluxe room would decline $5 each and raise the demand to 130 the lingo results are below
Lingo Linear Program
Model:
MAX=s1*30+s2*20+d1*30+d2*25+b2*40;
s1+d1<=100;
s2+d2+b2<=120;
d1+d2<=130;
s1+s2<=130;
b2<=50;
END
Global optimal solution found.
Objective value: 6750.000
Total solver iterations: 3
Variable Value Reduced Cost
S1 40.00000 0.000000
S2 0.000000 5.000000
D1 60.00000 0.000000
D2 70.00000 0.000000
B2 50.00000 0.000000
Row Slack or Surplus Dual Price
1 6750.000 1.000000
2 0.000000 30.00000
3 0.000000 25.00000
4 0.000000 0.000000
5 90.00000 0.000000
6 0.000000 15.00000
This scenario results in less profit for the management or $6750 verses $7000
Only 40 Super Savor are reserved and 130 Duplex are now reserved. Lingo points out a reduced cost of $5 for S2 to be considered. No this offer should not be considered.
Part D Solution
With a little work, an unused office area could be converted to a rental room. If the conversion cost is the same for both types of rooms, would you recommend converting the office to a Type I or a Type II room? Why
Type II is constrained and is more profitable and in demand to maximize profit
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