Healthy Living is an investment company that purchases old shopping malls and converts them into multi$-$purpose recreational facilities. The company recently purchased a regional mall. The total useable area is eight acres, and the company reserves $$800,000$ for repurposing the mall. The table below presents facilities, the area needed for them, the cost of building the facility, and its attraction.

Facility

Area

Cost $($in $$1000)$

Attraction

Weight$/$Strength

$2$

$$200$

$200$

Cardio Zone

$2$

$$100$

$250$

Basketball Court

$2\mathrm{.}5$

$$250$

$350$

Swimming Pool

$1$

$$200$

$200$

Badminton Court

$2\mathrm{.}5$

$$100$

$100$

Group Exercise Rooms

$1\mathrm{.}5$

$$50$

$150$

Squash Courts

$1\mathrm{.}5$

$$100$

$200$

There is only a single large area for either a basketball court or badminton court. The company is only willing to open a swimming pool when both weight$/$strength and cardio zone are built. The company wants to build either group exercise rooms or squash courts. There should be at least three different facilities.