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.

Month Space Required Duration Cost per sq ft. leased
March 30,000 1 $65
April 20,000 2 $100
May 40,000 3 $135

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

Step-by-step explanation:

days of the week

step-by-step explanation:

javier earned more money then kyle, so that won't always be a constant term, but the days of the week do not change so that term is always constant.

edit: i meant