Web Mercantile sells many household products through an on line 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 Leasing Period (months) Cost per Sq Ft Leased 1 30,000 sq ft 1 $65 2 20,000 sq ft 2 $100 3 40,000 sq ft 3 $135 4 10,000 sq ft 4 $160 5 50,000 sq ft 5 $190 The objective is to minimize the total leasing cost for meeting the space requirements a) Identify verbally the decisions to be made, the constraints on these decisions, and the overall measure of performance for the decisions b) Convert these verbal descriptions of the constraints and measure of performance into quantitative expressions in terms of the data and decisions c) Formulate a spreadsheet model for this problem Identify the data cells, the changing cells, the target cell, and the other output cells Also show the Excel equation for each output cell expressed as a SUMPRODUCT function d) Use the Excel Solver to solve the model e) Summarize the model in algebraic form by stating the decision variables, the objective function and constraints f) Hint Define your decision variables as Xij amount of space leased in month i for a period of j months for i 1, , 5 and j 1, , 6 i for example, X24 amount of space leased in month 2 for a period of 4 months This problem has 15 variables

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Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made

Web Mercantile sells many household products through an on-line 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

Leasing Period

(months)

Cost per Sq. Ft.

Leased

30,000 sq. ft.

$65

20,000 sq. ft.

$100

40,000 sq. ft.

$135

10,000 sq. ft.

$160

50,000 sq. ft.

$190

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

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

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

c) Formulate a spreadsheet model for this problem. Identify the data cells, the changing cells, the target cell, and the other output cells. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function.

d) Use the Excel Solver to solve the model.

e) Summarize the model in algebraic form by stating the decision variables, the objective function and constraints.

f) Hint: Define your decision variables as Xij = amount of space leased in month i for a period of j months for i = 1, , 5 and j = 1, , 6 i; for example, X24 = amount of space leased in month 2 for a period of 4 months. This problem has 15 variables.