NYNEX must schedule round-the-clock coverage for its telephone operators.To keep the number of different shifts down to a manageable level,it has only four different shifts.Operators work eight-hour shifts and can begin work at either midnight,8 a.m.,noon,or 4 p.m.Operators are needed according to the following demand pattern,given in four-hour time blocks. \[\begin{array} { | l | c | } \hline \text { Time Period } & \text { Operators Needed } \\ \hline \text { midnight to } 4 \text { a.m. } & 4 \\ \text { 4 a.m. to } 8 \text { a.m. } & 6 \\ 8 \text { a.m. to noon } & 90 \\ \text { Noon to } 4 \text { p.m. } & 85 \\ \text { 4 p.m. to } 8 \text { p.m. } & 55 \\ \text { 8 p.m. to midnight } & 29 \\ \hline \end{array}\] Formulate this scheduling decision as a linear programming problem,defining fully your decision variables and then giving the objective function and constraints.

Let X 1 = the number of telephone operator

Exam 21: Linear Programming

A site manager has three day laborers available for eight hours each and a burning desire to maximize his return on their wages.The site manager uses linear programming to assign them to two tasks and notes that he has enough work to occupy 21 labor hours.The linear program that the site manager has constructed has

(Multiple Choice)

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Question 41

________ is useful for allocating scarce resources among competing demands.

(Short Answer)

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Question 42

A binding constraint is the amount by which the left-hand side falls short of the right-hand side.

(True/False)

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Question 43

________ is the amount by which the left-hand side falls short of the right-hand side in a linear programming model.

(Short Answer)

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Question 44

NYNEX must schedule round-the-clock coverage for its telephone operators.To keep the number of different shifts down to a manageable level,it has only four different shifts.Operators work eight-hour shifts and can begin work at either midnight,8 a.m.,noon,or 4 p.m.Operators are needed according to the following demand pattern,given in four-hour time blocks. Time Period Operators Needed midnight to 4 a.m. 4 4 a.m. to 8 a.m. 6 8 a.m. to noon 90 Noon to 4 p.m. 85 4 p.m. to 8 p.m. 55 8 p.m. to midnight 29 Formulate this scheduling decision as a linear programming problem,defining fully your decision variables and then giving the objective function and constraints.

(Essay)

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Question 45

________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.

(Short Answer)

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Question 46

A binding constraint has slack but does not have surplus.

(True/False)

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Question 47

The interval over which the right-hand-side parameter can vary while its shadow price remains valid is the ________.

(Short Answer)

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Question 48

________ represent choices the decision maker can control.

(Short Answer)

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Question 49

The ________ is the upper and lower limit over which the optimal values of the decision variables remain unchanged.

(Short Answer)

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Question 50

The simplex method is an interactive algebraic procedure for solving linear programming problems.

(True/False)

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Question 51

A(n)________ is a value that the decision maker cannot control and that does not change when the solution is implemented.

(Short Answer)

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Question 52

A producer has three products,A,B,and C,which are composed from many of the same raw materials and subassemblies by the same skilled workforce.Each unit of product A uses 15 units of raw material X,a single purge system subassembly,a case,a power cord,three labor hours in the assembly department,and one labor hour in the finishing department.Each unit of product B uses 10 units of raw material X,five units of raw material Y,two purge system subassemblies,a case,a power cord,five labor hours in the assembly department,and 90 minutes in the finishing department.Each unit of product C uses five units of raw material X,25 units of raw material Y,two purge system subassemblies,a case,a power cord,seven labor hours in the assembly department,and three labor hours in the finishing department.Labor between the assembly and finishing departments is not transferable,but workers within each department work on any of the three products.There are three full-time (40 hours/week)workers in the assembly department and one full-time and one half-time (20 hours/week)worker in the finishing department.At the start of this week,the company has 300 units of raw material X,400 units of raw material Y,60 purge system subassemblies,40 cases,and 50 power cords in inventory.No additional deliveries of raw materials are expected this week.There is a $90 profit on product A,a $120 profit on product B,and a $150 profit on product C.The operations manager doesn't have any firm orders,but would like to make at least five of each product so he can have the products on the shelf in case a customer wanders in off the street. Formulate the objective function and all constraints,and clearly identify each constraint by the name of the resource or condition it represents.

(Essay)

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Question 53

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

(Short Answer)

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Question 54

A constraint is a limitation that restricts the permissible choices.

(True/False)

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Question 55

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

(True/False)

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Question 56

Which of the following statements regarding linear programming is NOT true?

(Multiple Choice)

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Question 57

Showing 41 - 57 of 57

________ is useful for allocating scarce resources among competing demands.

A binding constraint is the amount by which the left-hand side falls short of the right-hand side.

________ is the amount by which the left-hand side falls short of the right-hand side in a linear programming model.

________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.

A binding constraint has slack but does not have surplus.

The interval over which the right-hand-side parameter can vary while its shadow price remains valid is the ________.

________ represent choices the decision maker can control.

The ________ is the upper and lower limit over which the optimal values of the decision variables remain unchanged.

The simplex method is an interactive algebraic procedure for solving linear programming problems.

A(n)________ is a value that the decision maker cannot control and that does not change when the solution is implemented.

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

A constraint is a limitation that restricts the permissible choices.

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

Which of the following statements regarding linear programming is NOT true?

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