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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 five 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 five 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 $($Square Feet$)$

$130,000$

$220,000$

$340,000$

$410,000$

$550,000$

Month Cost per Square Feet Leased

$1$ $$65$

$2$ $$100$

$3$ $$135$

$4$ $$160$

$5$ $$190$

Click here for the Excel Data File

The objective is to minimize the total leasing cost for meeting the space requirements.

Formulate a spreadsheet model for this problem. Then use Solver to solve the model.

Determine the total cost.