Exam 20: Linear Programming

A constraint is a limitation that restricts the permissible choices.

Provide three examples of operations management decision problems for which linear programming can be useful,and why.

Briefly describe the meaning of a shadow price.Provide an example of how a manager could use information about shadow prices to improve operations?

The graphical method is a practical method for solving product mix problems of any size,provided the decision maker has sufficient quantities of graph paper.

Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible.She has decided to make her own cat food and has the following nutritional guidelines.Each four ounce portion must contain 22 units of protein,15 units of vitamin A,and 8 units of vitamin B.She has eggs,tomatoes,and chicken meat as possible inputs to her cat food.Each ounce of eggs contains 6 units of protein,4 units of Vitamin A,and 3 units of Vitamin B.Each ounce of tomatoes contains 1 unit of protein,8 units of Vitamin A,and 14 units of Vitamin B.Each ounce of chicken contains 22 units of protein,14 units of Vitamin A,and 8 units of Vitamin B.Chicken costs 40 cents per ounce,tomatoes cost 5 cents per ounce,and eggs cost 12 cents per ounce.To make the production process as easy as possible,she would like to make exactly four ounces of cat food from her recipe.Formulate this decision as a linear programming problem,defining fully your decision variables and then giving the objective function and constraints.

Use the graphical technique to find the optimal solution for this objective function and associated constraints. Maximize: Z=8A + 5B Subject To: Constraint 1 4A + 5B < 80 Constraint 2 7A + 4B < 120 A,B > 0 a.Graph the problem fully in the following space.Label the axes carefully,plot the constraints,shade the feasibility region,identify all candidate corner points,and indicate which one yields the optimal answer.

A(n)________ limits the ability to improve the objective function.

Table D.3 Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible.She has decided to make her own cat food and has the following nutritional guidelines.Each four ounce portion must contain 22 units of protein,15 units of vitamin A,and 8 units of vitamin B.She has eggs,tomatoes,and chicken meat as possible inputs to her cat food.Each ounce of eggs contains 6 units of protein,4 units of Vitamin A,and 3 units of Vitamin B.Each ounce of tomatoes contains 1 unit of protein,8 units of Vitamin A,and 14 units of Vitamin B.Each ounce of chicken contains 22 units of protein,14 units of Vitamin A,and 8 units of Vitamin B.Chicken costs 40 cents per ounce,tomatoes cost 5 cents per ounce,and eggs cost 12 cents per ounce. -Referring to Table D.3,an optimal four ounce serving contains 3.6 ounces of eggs and .4 ounce of tomatoes.Which of the following statements is best?

Table D.5 The Harper Company is in the process of production planning for the next four quarters.The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand.Anticipation inventory is also allowed,but not backorders.Undertime is paid,at a rate of $5.00 per unit.The beginning (or current)inventory is 25 units.Details are shown in the following POM for Windows table. -Use the information in Table D.5.Given the information in the optimal tableau,what is the inventory carrying cost,in dollars per unit per quarter?

What are the limitations of the graphical method of linear programming?

Table D.5 The Harper Company is in the process of production planning for the next four quarters.The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand.Anticipation inventory is also allowed,but not backorders.Undertime is paid,at a rate of $5.00 per unit.The beginning (or current)inventory is 25 units.Details are shown in the following POM for Windows table. -Use the information in Table D.5.What is the total cost of the optimal production plan?

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

You observe a linear programming problem that has been solved using the graphical method of linear programming.The feasible region and optimal solution are clearly labeled.How could you identify the slack or surplus amounts in the scenario?

A snack food producer runs four different plants that supply product to four different regional distribution centers.The division operations manager is focused on one product,so he creates a table showing each plant's monthly capacity and each distribution center's monthly demand (both amounts in cases)for the product.The division manager supplements this table with the cost data to ship one case from each plant to each distribution center.Formulate an objective function and constraints that will solve this problem using linear programming.

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

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

________ is useful for allocating scarce resources among competing demands.

A binding constraint has slack but does not have surplus.

Table D.5 The Harper Company is in the process of production planning for the next four quarters.The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand.Anticipation inventory is also allowed,but not backorders.Undertime is paid,at a rate of $5.00 per unit.The beginning (or current)inventory is 25 units.Details are shown in the following POM for Windows table. -Use the information in Table D.5.Given the information in the optimal tableau,what is the demand forecast for quarter 2?

A modeler is limited to two or fewer decision variables when using the ________.