After months of broken promises, partial payments, and general stupidity, the landlord had no choice but to evict the long term tenants that had become little more than squatters in his first rental property. As he surveyed the damage and pondered a mix of repairs and upgrades, he scoured the latest statistics on what different upgrades might in terms of increased rent. Beautifully refinishes wood floors could increase monthly rent about $100 and an upgrade to the kitchen would fetch $80 per month. The garage door needed replacement, but even though it would receive daily use, it was almost an order qualifier, and wouldn't net more than $20 per month. The house had always suffered from lack of back door- you had to access the backyard through the garage, so taking out a window and replacing it with a safety door would cost $250 and add only $15 to the monthly rent. The garage door would cost $350, the kitchen update would cost $1000 if he went with granite, and the floor refinish job would cost $400 to rent the buffer and buy the chemicals. It wouldn't be easy doing these upgrades; the garage door would take a half week, the back door one week, the floors two weeks and the tile three weeks.
There was another way around these jobs though; instead of doing then himself, the landlord could always hire a professional in each field that could finish the job in half the time but would charge a pretty penny for that speed. Refinishing floors would cost $2700, upgrading the kitchen would cost $2500, replacing the back window with a door would cost $600, and installing a garage door opener would cost $350. Total budget available is $3000 and job should be done no longer than 4 weeks.
Formulate an appropriate objective function for this scenario
If the variables are assigned as followed
X1 = contractor works on wood floors
x2= landlord works on wood floors
x3= contractor works on kitchen tile
x4= landlord works on kitchen tile
x5= contractor works on back door
x6= landlord works on back door
x7=contractor works on garage door
x8=landlord works on garage door