## (Solved) Calc 2 - Show all work for each problem that can be used for

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

c.Formulate a spreadsheet model for this problem. Identify the data cells, the changing cells, the target cell, and the other output cells. Please use the SUMPRODUCT function if possible. Use the Excel Solver to solve the model.

d.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.

Question 1

a.

x1 represents full time consultants

x2 represents part time consultants

x1

full time

shift1

shift 2

x2

part time

8

6

4

10

x3

limit

12

16

Constraints

a. x1+ x2 +x3 ? 12

b....

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This question was answered on: Oct 15, 2019

Solution~000.zip (25.37 KB)

STATUS

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Oct 15, 2019

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