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# Please You must follow the formatting instructions described in the file 1. Ten jobs are to be completed by three workers (Sam, Joy, and Kelly)...

Only need help with question 3, would really appreciate the help.

1 Please You must follow the formatting instructions described in the file 1. Ten jobs are to be completed by three workers (Sam, Joy, and Kelly) during the next week. Each person works up to 40 hours per week and is paid an hourly rate: Sam, Joy, and Kelly earn \$11, \$13, and \$14 per hour, respectively. Union rules require workers to be treated fairly; to ensure that most of the work is not assigned to one person while others are too idle, make sure that no person works more than 8 hours above any other worker. For example, if Joy works 20 hours, then Sam and Kelly should work within 12 to 28 hours, and Sam and Kelly should have work-hours that are no more than 8 hours apart. The times for the workers to complete the tasks are shown in the table below. The values in the cells assume that each task is completed by a single person. However, tasks can be shared with completion times being determined proportionally (e.g., if Joy and Kelly share task 1 equally, then Joy works 6 hours and Kelly works 9 hours). If no entry exists in a particular cell, it means that task cannot be performed by that worker. a. Formulate the problem as a linear optimization model (that is, define the variables, and write down the objective function and all constraints mathematically). b. Create a spreadsheet model for this problem and solve with Excel Solver. c. What is the optimal solution? What is the optimal value? 2. The director of a computer needs to schedule the staffing of the center. It is open from 8am 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 8am – Noon 6 Noon – 4pm 8 4pm – 8pm 12 8pm - 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 (8am – 4pm), afternoon (noon-8pm), and evening (4pm-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
2 many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost. a. Formulate the problem algebraically (i.e., define the variables, objective and constraints algebraically). b. Implement your model in Excel and solve it. c. What is the optimal solution? What is the optimal value? 3. Diana Dazzle, programming manager for GDUB-TV, must plan her schedule of television shows for next Wednesday evening. Of the nine one-half hour shows listed below, she must select exactly five for Wednesday evening. The estimated revenue (in \$ million) is given below for each show. Furthermore, the F.C.C. has classified each show as falling into one or more of the categories of Public Interest, Violence, Comedy, and Drama as given in the table below. ID # Show Revenue (\$ mill) Public Interest Violence Comedy Drama 1 Cheers 7 X X 2 Ghost 6 X X 3 Law and Order 8 X X X 4 Spiderman 5 X X X 5 Dharma and Greg 8 X 6 News Special:Middle East 3 X X 7 Focus on Science 4 X X 8 China Beach 7 X X 9 Urban Action for Education 2 X Diana's task is to select exactly five shows in order to maximize revenue. However, she must be mindful of the following limitations and issues: There must be at least as many shows aired that are categorized as drama as there are shows aired that are categorized as comedy. She cannot air more than two of the shows "News Special:Middle East", "Focus on Science" and "Urban Action for Education" (too serious!). If Diana airs "Focus on Science", she must air either "Spiderman" or "Law and Order" but not both. If she airs four or more shows in the violence category, she pays F.C.C. a fine of \$5 million, which will be deduced from the revenue. Formulate Diana Dazzle's selection problem as a binary optimization problem. Clearly define your decision variables, constraints, and objective function. Use only linear constraints and a linear objective function. You do not have to solve the model in Excel.
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This is a binary integer problem.
Decision Variables
we have 9 decision variables one for each show.
If the show is selected in optimal solution then value is
if the show is not selected in...

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