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.