Linear programming question( Graduate level)

1. A firm has just discovered that, for the next three months, it will have an insufficient supply of warehouse
space. The additional space requirements for the next three months are:
Month January February March
Space required (1000 sq. ft.) 25 10 20
To meet its requirements, the firm plans to lease additional space on a short-term basis. At the beginning
of each month, the firm can lease any amount of space for any number of months. Separate leases
can be taken out for different amounts of space and/or different lengths of time. For example, in the
first month, it might lease 20000 sq. ft. for 2 months, and another 5000 sq. ft. for 1 month. Also, new
leases may be taken out before the old ones expire. The costs per thousand square feet for leases of
various lengths are given by:
Length of lease 1 Month 2 Months 3 Months
Cost ($ per 1000 sq. ft.) 280 450 600
Formulate a linear program whose solution will provide a leasing policy that satisfies the space requirements
at minimum cost.
2. A manager for an outsourcing company has five jobs that can be performed by any of three contractors,
except that contractor #2 cannot perform job #4. The cost for each contractor to perform each job is
shown in the table below. Each job must be performed by exactly one contractor, and each contractor
may not perform more than two jobs. Formulate a linear programming problem to minimize the cost
of the assignments.
Contractors \ Jobs 1 2 3 4 5
1 8 6 5 7 4
2 6 5 3 2
3 7 8 5 6 3