Problem $4(20$ pts $)$

You're an intern at the Department of Transportation in the town of Abbac. Most of the town's houses are decaying, having been built in the early $1800\text{'}$s$.$ The mayor of Abbac is looking to replace these decaying houses with modern development with a tight budget of $$12,000,000.$ Each dilapidated house occupies a $0\mathrm{.}50-$acre lot $($was $0\mathrm{.}33$ before$).$ At most $300$ houses can be destroyed, at a cost of $$2000$ per house. Lot sizes for new single$-,$ double$-,$ and triple$-$family homes are $0\mathrm{.}18,0\mathrm{.}28,$ and $0\mathrm{.}4$ acres, fespectively. For each new home built, the required acreage should be increased by $15\%$ to account for the streets. At least $28\%$ of the modern development should be allocated to triple$-$family homes. At most $30\%$ should be allocated to single$-$and double$-$family homes. The construction cost per unit for single$-,$ double$-,$ and triplefamily homes is $$52,500,$$$72,900,$ and $$143,700,$ respectively. Building a single$-,$ double$-,$ and triple$-$family home will increase the town's happiness score by $8$ points, $5$ points, and $3$ points, respectively. Destroying an old home, however, decreases the town's happiness score by $4$ points.

a$)$ Based on the complete LP given for this problem in Homework $1$ Solutions $($and the slight modification in the problem statement$),$ solve the LP using Excel Solver. Provide a screenshot of the solved LP$,$ as well as of the Excel Solver window $($pre$-$solved$).(5$ pts $)$

b$)$ What's the minimum number of happiness points building a triple$-$family home can provide before it's no longer worth it to build triple$-$family homes $($round to $2$ decimal places$)?$ Without resolving the LP$,$ explain thoroughly and show work $($including screenshots of any reports used$).(5$ pts $)$

c$)$ What's the minimum number of happiness points building a double$-$family home must provide to start building some $($round to $2$ decimal places$)?$ Without re$-$solving the LP$,$ explain thoroughly and show work $($including screenshots of any reports used$).(5$ pts $)$

$2$

EM$333-$HW$2-$S$25$

d$)$ If the budget was increased by $$1,000,000,$ how will the town's happiness score be impacted? Without re$-$solving the LP$,$ explain thoroughly $($provide a value$)$ and show work $($including screenshots of any reports used$).(5$ pts$)$