Exam 19: Linear Programming

Table D.3 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.3.Given the information in the optimal tableau,what is the inventory carrying cost,in dollars per unit per quarter?

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.

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

Table D.3 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.3.What is the anticipation inventory at the end of the first quarter?

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.She used POM for Windows and received the following results.Provide an interpretation.

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.

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

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

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

In a linear programming model,the objective function answers the question What is to be maximized?

A very confused manager is reading a two-page report given to him by his student intern."She told me that she had my problem solved,gave me this,and then said she was off to her production management course," he whined."I gave her my best estimates of my on-hand inventories and requirements to produce,but what if my numbers are slightly off? I recognize the names of our four models W,X,Y,and Z,but that's about it.Can you figure out what I'm supposed to do and why?" You take the report from his hands and note that it is the answer report and the sensitivity report from Excel's solver routine. Explain each of the highlighted cells in layman's terms and tell the manager what they mean in relation to his problem.

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?

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

What is the meaning of a slack or surplus variable?

________ is useful for allocating scarce resources among competing demands.

Table D.2 Bahouth Enterprises produces a variety of hookahs for clients around the globe.Their small plant has a highly flexible workforce that can switch between products seamlessly.They forecast using a six-month planning period and have a demand forecast as shown in the table.The per-unit costs for each output option the sales and operations planner has at his disposal are indicated in the table.Regular output costs $40 per unit,overtime production is $60 per unit,and subcontracting is $70 per unit.Holding inventory from one month to the next costs $2 per unit per month and a backlog costs $5 per unit per month.Regular plant capacity is 300 units per month. -Use the information in Table D.2.The plant has no limits on the number of units produced by overtime or subcontractors and adopts a chase plan strategy for the six-month planning period.What is the cost for month 6 of their chase plan?

Table D.3 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.3.According to the optimal production plan,what is the overtime production in the second quarter?

One assumption of linear programming is that a decision maker cannot use negative quantities of the parameters.

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. Formulate this scheduling decision as a linear programming problem,defining fully your decision variables and then giving the objective function and constraints.

What does the feasible region represent?