Question

The Lotus Point Condo Project will contain both homes and apartments. The site can accommodateup to 10,000 dwelling units. The project must contain a recreation project: either a swimming-tenniscomplex or a sailboat marina, but not both. If a marina is built, then the number of homes in theproject must be at least triple the number of apartments in the project. A marina will cost $1.2 million,and a swimming-tennis complex will cost $2.8 million. The developers believe that each apartment willyield revenues with a net present value of $48,000, and each home will yield revenues with a net presentvalue of $46,000. Each home (or apartment) costs $40,000 to build. Formulate an integer program tohelp Lotus Point maximize profits.

Answer 1

Answer:

2,500 apartment and 7,500 house building the marina complex. This will provide the maximum yield.

Explanation:

Apartment Inflow PV 48,000

Home Inflow PV 46,000

Cost (for any) 40,000

Apartment NPV 48,000 - 40,000 = 8,000

Home NPV 46,000 - 40,000 = 6,000

As the house yield a lower profit it be better to keep the relationship at 1:3

As going above will decrease the profit

being 10,000 and a ratio of 1:3

we get that 10,000 x 1/4  = 2,500 apartment

and 10,000 x 3/4= 7,500 house

total profit:

2,500 x 8,000 + 7,500 x 6,000 - 1,200,000 = 5,300,000

If we build the swimming-tennis complex then we would build only apartment as they provide the max profit and there is no house quantity requirement:

total profit

10,000 x 8,000 - 2,800,000 = 5,200,000

The marina complex option yield the best result