After the government has managed to ban the operations of illegal small-scale mining in the Tarkwa area and the subsequent land reclamation, 40 acres of land have been made available to the Municipal assembly for the provision of various facilities for the communities. The assembly has set aside a budget of GH¢ 4,000,000 for this project and has charged a private developer to do this project. Three different types of facilities have been demanded by the assembly: gymnasium, children’s park, and market. The various unit committees of the assembly have demanded all together 8 gymnasiums, 4 children’s parks, and 6 markets. However, each type of facility costs a certain amount and requires a certain area to construct. A summary of these parameters together with the expected number of people using the facility weekly are given in Table 1.

Table 1 Facility	Cost (GH¢)	Acres Required	Expected usage of a facility (people/week)
Gymnasium	GH¢150,000	1.5	800
Children’s Park	GH¢200,000	2.4	1,000
Market	GH¢100,000	4	2,000

The assembly desires that the number of people using the facilities is maximised. The communities have about equal male and female population and the female tend to give preference to patronising the markets while the men prefer the gymnasiums. To balance female and male usage of facilities, the proportion of land that should be used for markets, with reference to community demand, should be the same proportion for gymnasium. Though the assembly is not using the project for profit making, it is to charge tolls of GH¢3, GH¢1 and GH¢2 for usage of market, children’s park 2 and gymnasium respectively to serve as a fund for facility maintenance. At least GH¢40,000 is expected by the assembly per week for maintenance. The private developer is interested in knowing the number of each type of facility to develop in order to meet the objectives of the assembly. 

Formulate this as a linear programming model.