Pendleton county plans to develop several new recreational facilities that must be completed within the $3\mathrm{.}5$ million budget. A survey of county residents has resulted in information about the types of facilities that county residents would like to see built, as described in the following table. The table also shows the cost to construct and maintain each facility, the acres each facility will require and the average monthly usage of each facility. The county has decided has decided that at least $15$ facilities will be built and has set aside $55$ acres to be used for construction.

Facility Cost Per Facility Acres per Facility People Per Month Annual Maintenance

Basketball Courts $300,00037003,000$

baseball fields $250,00051,0006,000$

Playgrounds $75,00028003,000$

Soccer Fields $175,00031,2007,000$

The county has also established the following list of ranked goals.

Rank $1$: It would like to spend the entire budget

Rank $2$: It would like to build enough facilities so that $15,000$ people or more each month can use them

Rank $3$: It wants to avoid using more than $55$ acres that have been set aside for the project

Rank $4$: It would like to avoid spending more than $$80,000$ per year on maintenance costs for the new facilities.

How many of each type of facility should be constructed.

GP Model $($use deviations$)$

label and define all variables of the problem; specify the

objective function and all constraints