Question

Suppose apartments are in four​ locations: Location​ A, Location​ B, Location​ C, and Location D. Location A is in the​ city, where your job is. Location B is 10 minutes farther from your job

than Location A. Location C is 10 minutes farther from your job than Location​ B, and Location D is 10 minutes farther than Location C. In​ turn, similar apartments in Location B rent for ​$105 less per month than apartments in Location​ A, apartments in Location C rent for ​$105 less than in Location​ B, and apartments in Location D rent for ​$105 less than in Location C. Suppose the value of your time is ​$16 per hour and you work 21 days per​ month, with each day requiring a​ round-trip commute from your apartment to work. For​ simplicity, assume rent and the opportunity cost of your time commuting to work are the only factors influencing the location in which to rent an apartment. You should rent an apartment in ▼ Location C Location A Location B Location D .

Answer 1

You should rent an apartment in :
Location D

Reason - At location A, suppose the rent is $X , and the time taken to reach the job from your apartment is Y minutes(Y<10 minutes).
As we move to location B, C and D, the time taken to commute to the job will increase to be Y+10, Y+20 and Y+30 minutes respectively.
While, assuming, the rent to be decreasing as we move from A to B,C and D, the rent for B would be $(X-105), C would be $(X-210) and D would be $(X-315). Since, the rent will be lowest at location D, and value of time per minute of extra commute would be $0.27 (Assuming per hour value to be $16) , the opportunity cost of time will be lowest at Location D ( i.e. opportunity cost = (Cost of rent at location D) / (Cost of time taken to commute).
Hence, location D should be preferred.