Question

In the fall, Jay Thompson decided to live in a university dormitory. He signed a dorm contract under which he was obligated to pay the room rent for the full college year. One clause stated that if he moved out during the year, he could sell his dorm contract to another student who would move into the dormitory as his replacement. The dorm cost was $5000 for the two semesters, which Jay had already paid A month after he moved into the dorm, he decided he would prefer to live in an apartment. That week, after some searching for a replacement to fulfill his dorm contract, Jay had two offers. One student offered to move in immediately and to pay Jay $300 per month for the eight remaining months of the school year. A second student offered to move in the second semester and pay $2500 to Jay. Jay estimates his food cost per month is $500 if he lives in the dorm and $450 if he lives in an apartment with three other students. His share of the apartment rent and utilities will be $390 per month. Assume each semester is 4.5 months long. Disregard the small differences in the timing of the disbursements or receipts. What is the cost of the cheapest alternative?

Answer 1

To determine the cost of the cheapest alternative, we compare the costs of living in the dormitory and living in the apartment. The cheapest alternative for Jay would be to live in the apartment.

Step-by-step explanation:

To determine the cost of the cheapest alternative, we need to compare the costs of living in the dormitory and living in the apartment. Let's calculate the costs for each option:

• Dormitory option: Jay has already paid $5000 for the two semesters. For the remaining eight months, he can either receive $300 per month or $2500 for the second semester. Jay's food cost per month in the dorm is $500, so his total cost would be $5000 + ($300 * 8) - ($500 * 8) = $8,800. If he chooses the $2500 offer for the second semester, his total cost would be $5000 + $2500 - ($500 * 8) = $7,900.
• Apartment option: Jay's monthly food cost would be $450, and his share of the apartment rent and utilities would be $390 per month. So his total cost for eight months would be ($450 * 8) + ($390 * 8) = $7,680.

Comparing the costs, the cheapest alternative for Jay would be to live in the apartment.

Answer 2

The cheapest alternative is: $300 a month immediately.

Step-by-step explanation:

Giving the following information:

The dorm cost was $5000 for the two semesters

Jay had already paid a month after he moved into the dorm.

Jay estimates his food cost per month is $500 if he lives in the dorm and $450 if he lives in an apartment.

His share of the apartment rent and utilities will be $390 per month.

Each semester is 4.5 months long.

Alternative A:

One student offered to move in immediately and to pay Jay $300 per month for the eight remaining months of the school year.

Income= 300*8= 2400

Apartment rent= (3120)

Food= (3600)

Total= (4320)

Alternative B:

A second student offered to move in the second semester and pay $2500 to Jay.

Income= 2500

Dorm rent= (5000/9)*3.5= (1944)

Apartment rent= (1755)

Dorm food= 500*3.5= (1750)

Apartment food= (2025)

Total= (4974)

Alternative C:

Stay in the dorms

Dorm rent= (4444.44)

Dorm Food= (4000)

Total= $8444.44

The cheapest alternative is A.