Web Mercantile sells many household products through an online catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most economical to lease only the amount needed each month on a month-by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month.
The space requirement and the leasing costs for the various leasing periods are as follows:
|Month||Required Space (Sq. Ft.)||Leasing Period (Months)||Cost per Sq. Ft.Leased|
The objective is to minimize the total leasing cost for meeting the space requirements.
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Formulate a linear programming model for this problem.
minimize C = (Click to select) 160 65 190 100 135 (x11 + x21 + x31 + x41 + x51) + (Click to select) 100 135 160 190 65 (x12 + x22+ x32 + x42) + (Click to select) 190 135 160 65 100 (x13 + x23 + x33) + (Click to select) 190 100 135 160 65 (x14 + x24) + (Click to select) 135 100 65 190 160 x15
subject to x11 + x12 + x13 + x14 + x15 = (Click to select) 48000 18000 58000 28000 38000
x15 + x24 + x33 + x42 + x51 = (Click to select) 38000 28000 58000 48000 18000
x14 + x15 + x23 + x24 + x32 + x33 + x41 + x42 = (Click to select) 58000 18000 38000 28000 48000
x12 + x13 + x14 + x15 + x21 + x22 + x23 + x24 = (Click to select) 38000 48000 18000 58000 28000
x12 + x13 + x14 + x15 + x21 + x22 + x23 + x24 = (Click to select) 18000 38000 48000 58000 28000