Instructions:

1. For each question, your mathematical model and answers to each individual part should be typed in Microsoft Word. Also, for each question, state your model by clearly defining your decision variables (with appropriate units), the objective function (min or max), and all the relevant (including the nonnegativity) constraints.
2. Excel spreadsheet models are required for each question. You can submit a workbook containing all the separate spreadsheets. Make sure that each spreadsheet carries the name of the question you are answering.
3. For how to use the Solver for solving linear programming models and produce the Solver’s sensitivity report, refer to Appendix 2.2 page 89 and Appendix 3.1 page 149 in your textbook 14e, respectively.
4. For Questions 3 and 4 use the information summarized in the Solver’s sensitivity report as much as you can to answer the sensitivity analysis questions.

Question #1:

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 #2:

Larry Edison is the Director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 AM until midnight. Larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required:
Time of Day Minimum Number of Consultants Required to be on Duty

8 AM -noon 4
Noon – 4 PM 8
4 PM – 8 PM 10
8 PM – Midnight 6

Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecutive hours in any of the following shifts: morning (8 AM – 4 PM), and evening (4 PM – Midnight). Full-time consultants are paid $14.00 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12.00 per hour.
An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty.
Larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost.
a) Formulate a linear programming model for this problem on a spreadsheet. Use the Solver to solve this model.

b) Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints.
Question #3:

Answer questions 1 to 5 under managerial report for Case Problem: PRODUCT MIX given on page 146-147

Question #4: Problem 21 page 139

Instructions:

1. For each question, your mathematical model and answers to each individual part should be typed in Microsoft Word. Also, for each question, state your model by clearly defining your decision variables (with appropriate units), the objective function (min or max), and all the relevant (including the nonnegativity) constraints.
2. Excel spreadsheet models are required for each question. You can submit a workbook containing all the separate spreadsheets. Make sure that each spreadsheet carries the name of the question you are answering.
3. For how to use the Solver for solving linear programming models and produce the Solver’s sensitivity report, refer to Appendix 2.2 page 89 and Appendix 3.1 page 149 in your textbook 14e, respectively.
4. For Questions 3 and 4 use the information summarized in the Solver’s sensitivity report as much as you can to answer the sensitivity analysis questions.

Question #1:

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 #2:

Larry Edison is the Director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 AM until midnight. Larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required:
Time of Day Minimum Number of Consultants Required to be on Duty

8 AM -noon 4
Noon – 4 PM 8
4 PM – 8 PM 10
8 PM – Midnight 6

Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecutive hours in any of the following shifts: morning (8 AM – 4 PM), and evening (4 PM – Midnight). Full-time consultants are paid $14.00 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12.00 per hour.
An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty.
Larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost.
a) Formulate a linear programming model for this problem on a spreadsheet. Use the Solver to solve this model.

b) Summarize the model in algebraic form by defining the decision variables, the objective function and all the constraints.
Question #3:

Answer questions 1 to 5 under managerial report for Case Problem: PRODUCT MIX given on page 146-147

Question #4: Problem 21 page 139