Problem 6. (25 total points) Professor Scutari is so proud of your grade on the

Question

Problem 6. (25 total 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, building materials, etc. A local company offers warehouse space based on monthly usage. You need to set up an LP to find the cheapest way to store what is needed. Below is a chart of the space you need for each month. Next to it is 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 DurationCost per Sq. ft. leased (months) Mbnth Space Required March April20,000 May $65 $100 $135 30,000 40,000

Explanation / Answer

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 upto 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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