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1. The postal employee scheduling example is called a static scheduling model because we assume that the post office faces the same situation each week. In reality, demands change over time, workers take vacations in the summer, and so on, so the post office does not face the same situation each week. A dynamic scheduling model (not covered) is necessary for such problems.

2. In the Barney-Jones investment model, increase the maximum amount allowed in any investment to $150,000. Then run a one-way sensitivity analysis to the money market rate in cash. Capture one output variable: the maximum amount of cash ever put in the money market. You can choose any reasonable range for varying the money market rate.

3. A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; 75 drivers in year 5. At the beginning of each year; the bus company must decide how many drivers to hire or fire. It costs It costs $4000 to hire a driver and $2000 to fire a driver. A driver’s salary is $10,000 per year. At the beginning of year 1, the company has 50 drivers. A driver hired at the beginning of a year can be used to meet the current year’s requirement and is paid full salary for the current year.

a. Determine how to minimize the bus company’s salary, hiring, and firing costs over the next five years.

b. Use SolverTable to determine how the total number hired, total number fired, and total cost change as the unit hiring and firing costs each increase by the same percentage.

4. During each four-hour period, the Smalltown police force requires the following number of on-duty police officers: eight from midnight to 4AM; seven from 4AMto 8AM; six from 8AMto noon; six from noon to 4PM; five from 4PM to 8PM; and four from 8PM to midnight. Each police officer works two consecutive four-hour shifts.

a. Determine how to minimize the number of police officers needed to meet Smalltown’s daily requirements.

b. Use Solvertable to see how the number of police officers changes as the number of officers needed from midnight to 4AM changes.

5. A chemical company produces three products, A,B,and C, and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $55; C,$100. Producing a unit of A requires one hour of labor; a unit of B, two hours of labor plus two units of A; and a unit of C, three hours of labor plus one unit of B. Any A that is used to produce B cannot be sold. Similarly, any B that is used to produce C cannot be sold. A total of 4000 hours of labor is available. Only as many as 500 units of product C can be sold. Determine how to maximize the company’s revenue?

6. Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 100,000 pounds of grade 9 oranges and 120,000 pounds of grade 6 oranges on hands. The average quality of oranges sold in bags must be at least 7, and the average quality of oranges used to produce orange juice must be 8. Each pound of oranges that is used for juice yields a revenue of $1.50 and incurs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of $1.05. Each pound of oranges sold in bags yields a revenue of $1.50 and incurs a variable cost of $0.70.

a. Determine how Sunblessed can maximize its profit.

b. Use SolverTable to determine how a change in the cost per bag of oranges changes the optimal solution.

c. Use SolverTable to determine how a change in the amount of grade 9 oranges available affects the optimal solution.

d. Use SolverTable to determine how a change in the required average quality required for juice changes the optimal solution.

1. The postal employee scheduling example is called a static scheduling model because we assume that the post office faces the same situation each week. In reality, demands change over time, workers take vacations in the summer, and so on, so the post office does not face the same situation each week. A dynamic scheduling model (not covered) is necessary for such problems.

2. In the Barney-Jones investment model, increase the maximum amount allowed in any investment to $150,000. Then run a one-way sensitivity analysis to the money market rate in cash. Capture one output variable: the maximum amount of cash ever put in the money market. You can choose any reasonable range for varying the money market rate.

3. A bus company believes that it will need the following numbers of bus drivers during each of the next five years: 60 drivers in year 1; 70 drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; 75 drivers in year 5. At the beginning of each year; the bus company must decide how many drivers to hire or fire. It costs It costs $4000 to hire a driver and $2000 to fire a driver. A driver’s salary is $10,000 per year. At the beginning of year 1, the company has 50 drivers. A driver hired at the beginning of a year can be used to meet the current year’s requirement and is paid full salary for the current year.

a. Determine how to minimize the bus company’s salary, hiring, and firing costs over the next five years.

b. Use SolverTable to determine how the total number hired, total number fired, and total cost change as the unit hiring and firing costs each increase by the same percentage.

4. During each four-hour period, the Smalltown police force requires the following number of on-duty police officers: eight from midnight to 4AM; seven from 4AMto 8AM; six from 8AMto noon; six from noon to 4PM; five from 4PM to 8PM; and four from 8PM to midnight. Each police officer works two consecutive four-hour shifts.

a. Determine how to minimize the number of police officers needed to meet Smalltown’s daily requirements.

b. Use Solvertable to see how the number of police officers changes as the number of officers needed from midnight to 4AM changes.

5. A chemical company produces three products, A,B,and C, and can sell these products in unlimited quantities at the following unit prices: A, $10; B, $55; C,$100. Producing a unit of A requires one hour of labor; a unit of B, two hours of labor plus two units of A; and a unit of C, three hours of labor plus one unit of B. Any A that is used to produce B cannot be sold. Similarly, any B that is used to produce C cannot be sold. A total of 4000 hours of labor is available. Only as many as 500 units of product C can be sold. Determine how to maximize the company’s revenue?

6. Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 100,000 pounds of grade 9 oranges and 120,000 pounds of grade 6 oranges on hands. The average quality of oranges sold in bags must be at least 7, and the average quality of oranges used to produce orange juice must be 8. Each pound of oranges that is used for juice yields a revenue of $1.50 and incurs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of $1.05. Each pound of oranges sold in bags yields a revenue of $1.50 and incurs a variable cost of $0.70.

a. Determine how Sunblessed can maximize its profit.

b. Use SolverTable to determine how a change in the cost per bag of oranges changes the optimal solution.

c. Use SolverTable to determine how a change in the amount of grade 9 oranges available affects the optimal solution.

d. Use SolverTable to determine how a change in the required average quality required for juice changes the optimal solution.

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