Question

Solve the following optimal apartment location problem using optimization in differences

Suppose you narrowed your apartment list to four. Those 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 amounts to 7 hours more of commuting per month than Location A. Location C amounts to 7 hours more of commuting per month than Location​ B, and Location D amounts to 7 hours more of commuting per month than than Location C.

In​ turn, similar apartments in Location B rent for ​$185 less per month than apartments in Location​ A, apartments in Location C rent for $185 less than in Location​ B, and apartments in Location D rent for ​$185 less than in Location C. Suppose the value of your time is ​$16 per hour.

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.

Using optimization in differences and Location A as your starting point

A) You should rent an apartment in _______

Suppose you currently rent an apartment in Location C.

B) By moving to​ optimize, you change your net benefit by $_______

Answer 1

Please see the caluclations below:
Assuming Rent at A to be x, and the travel cost being 7 hours * 16 per hour = $ 112.

(a) From below, lowest cost occurs at D (x-555 + 336 = x-219)

(b) Moving from C to D, we save: 219-146= 73

	Travel Cost	Rent	Total Cost
A	0	x	x
B	112	x-185	x-73
C	224	x-370	x-146
D	336	x-555	x-219

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