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Problem 2 (25 points)

Professor Scutari is so proud of your grade on the first midterm that he gets you a job with Purdue Facilities. They are rebuilding our beloved Grissom Hall. For the next three months, they need to store extra equipment and building materials. A local company offers warehouse space based on monthly usage. You need to set up a linear program (LP) to find the cheapest way to store what is needed.

Below is a chart of the space you need for each month, along with a chart of the leasing options—the total price per square foot leased and the corresponding duration. Note that you may have multiple, overlapping leases (e.g., two one-month leases for March and April, and a two-month lease starting in April). All leases should end by May. You may lease more space than required.

Monthly Space Requirements:
- March: 30,000 square feet
- April: 20,000 square feet
- May: 40,000 square feet

Leasing Options:
- Duration: 1 month, Cost: $65 per square foot
- Duration: 2 months, Cost: $100 per square foot
- Duration: 3 months, Cost: $135 per square foot

Set up an LP to determine the cheapest leasing strategy.

Answer :

Answer:

Step-by-step explanation:

We will use this notation:


x0: The space leased only for March.

x1: The space leased only for April.

x2: The space leased only for May.

x3: The space leased for March and April.

x4: The space leased for April and May.

x5: The space leased for March, April, and May.


Note that there can be up to 3 leases for March, 4 leases for April, and 3 leases for May. The LP model will be:


Minimise 65x0+65x1+65x2+100x3+100x4+135x5

s.t.

x0+x3+x5>=30000 # space leased for March is atleast 30,000 sq.ft

x1+x3+x4+x5>=20000 # space leased for April is atleast 20,000 sq.ft

x2+x4+x5>=40000 # space leased for May is atleast 40,000 sq.ft

x0,x1,x2,x3,x4,x5>=0


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Rewritten by : Barada