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Minimum Number of Consultants Required to Be on Duty Time of Day 8 AM-noon Noon-4 PM 4 PM-8 PM 8 12 8 PM-midnight Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 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 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. Which category of linear programming problem does this problem fit? Why? E* b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form.

Minimum Number of Consultants Required to Be on Duty Time of Day 8 AM-noon Noon-4 PM 4 PM-8 PM 8 12 8 PM-midnight Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 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 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. Which category of linear programming problem does this problem fit? Why? E* b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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need the answers for 3.15 and 3.16

of Chapter 3 Problems 103 ld The objective is to minimize the total leasing cost for meet- ing the space requirements. Minimum Number of a. Indicate why this is a cost-benefit-trade-off prob- lem by identifying both the activities and the bene- fits being sought from these activities. Consultants Required to Be on Duty Time of Day 8 AM-noon b. Identify verbally the decisions to be made, the con- straints 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 target cell, and the other output cells. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function. Then use the Excel Solver to solve the model. Noon-4 PM 8. 4 PM-8 PM 12 8 PM-midnight 6 Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 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 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- E* e. Summarize the model in algebraic form. E*3.14. Consider the following algebraic formulation of a cost-benefit-trade-off problem involving three benefits, where the decisions to be made are the levels of four activities (A1, A2, A3, and A4): time consultants should work each shift to meet the above requirements at the minimum possible cost. Minimize Cost 2 A, + A2 - A3 + 3 A4 a. Which category of linear programming problem does this problem fit? Why? b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form. 3.16.* The Medequip Company produces precision med- ieal diagnostic equipment at two factories. Three medical centers have placed orders for this month's production out- put. The following table shows what the cost would be for shipping each unit from each factory to each of these cus- tomers. Also shown are the number of units that will be pro- duced at each factory and the number of units ordered by subject to E* Benefit 1: 3 A,+2 A2-2 A3+5 A4 > 80 (minimum acсeptable level) + A4> 10 (minimum Benefit 2: A1- A2 acсеptable level) A1 + A2- A, + 2A42 30 (minimum acceptable level) Benefit 3: each customer. and A decision now needs to be made about the shipping A, 20 A, 2 0 A4 2 0 plan for how many units to ship from each factory to each customer. Formulate and solve the spreadsheet model for this problem. Unit Shipping Cost To From Customer 1 Customer 2 Customer 3 Output $700 400 units Factory 1 Factory 2 $600 $800 400 900 600 500 units Order size 300 units 200 units 400 units a. Which category of linear programming problem does this problem fit? Why? b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize this formulation in algebraic form. E* Larry Edison is the Director of the Computer Center for 3.15 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 deter- mined that the following number of computer consultants are required: The Fagersta Steelworks currently is working two mines to obtain its iron ore. This iron ore is shipped to either of two storage facilities. When needed, it then is shipped on to the 3.17. s from
Transcribed Image Text:of Chapter 3 Problems 103 ld The objective is to minimize the total leasing cost for meet- ing the space requirements. Minimum Number of a. Indicate why this is a cost-benefit-trade-off prob- lem by identifying both the activities and the bene- fits being sought from these activities. Consultants Required to Be on Duty Time of Day 8 AM-noon b. Identify verbally the decisions to be made, the con- straints 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 target cell, and the other output cells. Also show the Excel equation for each output cell expressed as a SUMPRODUCT function. Then use the Excel Solver to solve the model. Noon-4 PM 8. 4 PM-8 PM 12 8 PM-midnight 6 Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecu- tive hours in any of the following shifts: morning (8 AM-4 PM), afternoon (noon-8 PM), and evening (4 PM-midnight). Full-time consultants are paid $14 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 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- E* e. Summarize the model in algebraic form. E*3.14. Consider the following algebraic formulation of a cost-benefit-trade-off problem involving three benefits, where the decisions to be made are the levels of four activities (A1, A2, A3, and A4): time consultants should work each shift to meet the above requirements at the minimum possible cost. Minimize Cost 2 A, + A2 - A3 + 3 A4 a. Which category of linear programming problem does this problem fit? Why? b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize the model in algebraic form. 3.16.* The Medequip Company produces precision med- ieal diagnostic equipment at two factories. Three medical centers have placed orders for this month's production out- put. The following table shows what the cost would be for shipping each unit from each factory to each of these cus- tomers. Also shown are the number of units that will be pro- duced at each factory and the number of units ordered by subject to E* Benefit 1: 3 A,+2 A2-2 A3+5 A4 > 80 (minimum acсeptable level) + A4> 10 (minimum Benefit 2: A1- A2 acсеptable level) A1 + A2- A, + 2A42 30 (minimum acceptable level) Benefit 3: each customer. and A decision now needs to be made about the shipping A, 20 A, 2 0 A4 2 0 plan for how many units to ship from each factory to each customer. Formulate and solve the spreadsheet model for this problem. Unit Shipping Cost To From Customer 1 Customer 2 Customer 3 Output $700 400 units Factory 1 Factory 2 $600 $800 400 900 600 500 units Order size 300 units 200 units 400 units a. Which category of linear programming problem does this problem fit? Why? b. Formulate and solve a linear programming model for this problem on a spreadsheet. c. Summarize this formulation in algebraic form. E* Larry Edison is the Director of the Computer Center for 3.15 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 deter- mined that the following number of computer consultants are required: The Fagersta Steelworks currently is working two mines to obtain its iron ore. This iron ore is shipped to either of two storage facilities. When needed, it then is shipped on to the 3.17. s from
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