1. (20) Eric Cartman is the CEO of South Park Loading Company, which needs to le

Question

1. (20) Eric Cartman is the CEO of South Park Loading Company, which needs to lease warehouse space over the next 3 months. The space requirement for each of the three months (in thousands of square feet) are: month 1 15, month 2-13, and month 3- 17. The leasing costs depend on the length of the lease. The monthly leasing costs (in dollars per thousand square feet) for various lengths of the lease are: 1-month lease - 280, 2-month lease 245, and 3-month lease 220. Cartman can lease any amount of space for any length he wants within the three-month period (so, he cannot take a 2-month lease at the start of the third month for instance). Also, he could start two or more leases of different lengths at the same time. Formulate an LP which Cartman could use to figure out the leasing schedule which will minimize the total costs that he will incur

Explanation / Answer

The above information can be represented as

Minimize Z = 280 (m11) + 490 (m12 +m13) +660 (m11+m12+m13) - Total Cost

Subject to the constraints 'X'

m11+m12+m13 >= 15 (Space requrie for 1 month)

m12+m13+m21+m22 >= 13 (Space requrie for 2 month)

m13 +m22+m31 >= 17 (Space requrie for 3 month)

x>=0, y>=0

Length of Lease 1 Month 2 Month 3 Month Total Cost 1 Month           280               -                 -                280 2 Month           245           245               -                490 3 Month           220           220           220              660 Space Requirement (in '000' of Sq. Ft.)              15              13              17

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