Question

Adventures & Vacations LLC bought a parcel of land and plans to build luxury villas on the property. The owners of the company plans to build four types of villas: deluxe non-smoking villas, deluxe villas that allow smoking, premier non-smoking villas and premier villas that allow smoking.

Your team works for a consultant company that was hired to help the company plan the how many rooms of each type to build. You were given these following information by Adventures & Vacations LLC:

1. Considering the industry trends, villas that allow smoking should be more more than 50% of the number of non-smoking rooms.
2. There should be at least 100 but no more than 180 deluxe rooms
3. Estimated construction costs the types of rooms are as follows: Deluxe villa = $12,000 and Premier villa = $15,000. Any villa that allow smoking will have additional systems and equipment added such as multiple smoke detectors, fire extinguishers, sprinklers and air purifiers. The estimated cost of this additional system is $3000. Adventures and Vacations LLC already raised $6.3 million in construction guarantees for this portion of the building.
4. The expected per night revenues for the villas are: $130 for Deluxe villas and $175 for Premier villas. These prices are for non-smoking rooms. Guests will be charged an extra $15 per room if they choose to stay at villas that allow smoking.
5. After consulting with the architect, the most aesthetically viable design for the property require that the number of deluxe rooms be at least 1.5 times the number of the premier rooms, but no more than 2.5 times.

Instructions:

1) Your team's job is to design the LP model to help Adventures and Vacations LLC determine the best mix of rooms to construct.

Note: Show your complete LP model for this problem. There is no need to solve. Make sure to include the following:

• Objective Function
• Constraints

2) Briefly discuss your rationale or reasoning for the LP model you are recommending.

3) What were some of the challenges you experienced when you were formulating the model?

Answer 1

Q1.

Variable definition :

Number of non-smoking Deluxe villas = NSD

Number of smoking Deluxe villas = SD

Number of non-smoking premier villas = NSP

Number of smoking premier villas = SP

Objective function:

Revenue per night for Smoking Deluxe = 130 + 15 = 145

Revenue per night for Smoking Premier = 175 + 15 = 190

As consultant for Adventures & Vacations LLC, we'd like to maximize revenue for the client.

Total revenue per day = 130*NSD + 145*SD + 175*NSP + 190*SP

Constraints:

SD + SP > 50%*(NSD + NSP)

SD + SP > 0.5*(NSD + NSP) .......Constraint as villas that allow smoking should be more more than 50% of the number of non-smoking rooms

SD + NSD >=100 .......Constraint as there should be at least 100 deluxe rooms

SD + NSD <=180 .......Constraint as there should be no more than 180 deluxe rooms

Cost for Smoking Deluxe villa= 12000 + 3000 = 15000

Cost for Smoking Premier villa= 15000 + 3000 = 18000

NSD*12000 + SD*15000 + NSP*15000 + SP*18000 <= 6300000 ........Contraint as budget constraint of $6.3 Million

SD + NSD >= 1.5*(SP + NSP) .......Constraint as number of deluxe rooms be at least 1.5 times the number of the premier rooms

SD + NSD <= 2.5*(SP + NSP) .......Constraint as number of deluxe rooms be no more than 2.5 times the number of the premier rooms

SD, NSD, SP, NSP >=0 .........Non-negativity constraint as number of villas cannot be negative