Mr. Trace Huels
Dec 01, 2024
Web Mercantile sells many household products through an online catalog. The company needs substantial warehouse space for storing
Web Mercantile sells a variety of household products through an online catalog. To effectively manage its inventory, the company requires substantial warehouse space for storing its goods. Over the next five months, plans are in place to lease this warehouse storage space. The monthly space requirements are known, but they vary significantly from month to month.
Given these differing space requirements, it may be more economical to lease only the amount of space needed for each month on a month-by-month basis. However, the additional cost of leasing space for subsequent months is considerably less than for the first month, which raises the possibility that leasing the maximum space required for the entire five-month period could be more cost-effective.
Alternatively, the company could consider an intermediate approach, adjusting the total amount of space leased—either by adding a new lease or allowing an old lease to expire—at least once during the rental period, but not every month.
The space requirements and leasing costs for the various leasing periods are as follows:
Month | Required Space (Sq. Ft) 1 | 30,000 2 | 20,000 3 | 40,000 4 | 10,000 5 | 50,000
Leasing Period (Months) | Cost per Sq. Ft Leased 1 | $65 2 | $100 3 | $135 4 | $160 5 | $190
The objective is to minimize the total leasing cost while adequately meeting the space requirements.
(A) Please formulate a linear programming model for this problem.
(B) Solve this model using the simplex method.
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