A company needs to lease warehouse storage space

A company needs to lease warehouse storage space for five months at the start of the year. The space requirements (in square feet) and the leasing costs of each type of lease are given in the two tables below:
Month Required Space (sq. feet)
Jan 15,000
Feb 10,000
Mar 20,000
Apr 5,000
May 25,000

Lease Term
(months) Cost per 1,000 sq. feet leased
1 $280
2 $450
3 $600
4 $730
5 $820

Leases for different terms can begin at the same time. In addition, a lease should not be entered into if its term extends past May.
(a) Create and solve a linear programming model for determining the leasing schedule that provides the required amounts of space at minimum cost.
(b) What would the impact of a 1,000 square foot increase in the space required for each of the months from January to May?

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