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.

_____________________________ Required Space

Month ________________________ (Square Feet)

1 ................................................ 30,000

2 ................................................ 20,000

3 ................................................ 40,000

4 ................................................ 10,000

5 ................................................ 50,000

Leasing Period_____________________________ Cost per

(Months) ______________________________ Sq. Ft. Leased

1 .............................................. $ 65

2 .............................................. 100

3 .............................................. 135

4 .............................................. 160

5 .............................................. 190

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

a. Indicate why this is a cost-benefit-trade-off problem by identifying both the activities and the benefits being sought from these activities.

b. Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions.

c. Convert these verbal descriptions of the constraints and the measure of performance into quantitative expressions in terms of the data and decisions.

d. Formulate a spreadsheet model for this problem. Identify the data cells, the changing cells, the objective cell, and the other output cells. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function. Then use Solver to solve the model.

e. Summarize the model in algebraic form?