Question

Resource constraints: $120,000 budget; 12 acres of land. Selection constraint: either swimming pool or tennis center can be constructed (not both). Expected Usage (people/day) Land Requirement (acres) Cost ($) 4 Recreation Facility Swimming pool Tennis Center Athletic field Gymnasium 300 90 400 150 35,000 10,000 25,000 90,000 2 7 3

The council wants to construct facilities that will maximize the expected daily usage by the residents of the community.

Formulate this problem

Answer 1

uts to u x + 2x2 + 7x2 + 3xy s 12 acres Ans. The community has a 1,20,000 construction budget and 12 acre of land The Swimming pool and tennis center must be built on the same part of the land parcel; there for only one of those two facilities can be constructed. The council Wa- know which of the recreation facilities to construct in order to maximize the expec- fed daily usage. The model usage. The model yor this for this problem is for inculated as follows: Expected usage I cost Land Require- ( mauf l'acres) 3.00 35000 Swimming pool Tennis center Athletic field Gymnasium 90000 300x, & 90x2 + 400 x3 Subject to : 35000x + 10 000x2 + 250 20x2 + 90000 xy E120000 Recreation facility i people I Day) no 10 ODO که م له yoo 25000 3 Z Max t 150xu X3 X 시 Xe + xq el facility X, Xa ,XB, Xy or)

where, X, Construction of a Swimming Pool X2 construction of a tennis center X2 cous fruction of athlete field Xч construction of а a gymnasium