Reference no: EM133085861

A small town wants to build some new recreational facilities. The proposed facilities include a swimming pool, recreation center, basketball court and baseball field. The town council wants to provide the facilities which will be used by the most people, but faces budget and land limitations. The town has $400,000 and 14 acres of land. The pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. Also the council has only enough flat land to build the basketball court or the baseball field. The daily usage and cost of the facilities (in $1,000) are shown below.

Variable	Facility	Usage	Cost ($1,000)	Land
X1	Swimming pool	500	100	2
X2	Recreation center	450	200	3
X3	Basketball court	300	150	4
X4	Baseball field	200	100	5

The mathematical formulation of this ILP problem is given below:

MAX: 500 X1 + 450 X2 + 300 X3 + 200 X4

Subject to:        

100 X1 + 200 X2 + 150 X3 + 100 X4 ≤ 400 (budget)

2 X1 + 3 X2 + 4 X3 + 5 X4 ≤ 14  (land)

X1 - X2 ≤ 0  (pool & recreation center)

X3 + X4 ≤ 1  (basketball and baseball)

Xi ≥ 1

Xi = 0, 1

Use Solver to find the maximum possible value of the objective function of this ILP problem