Exam 4: Linear Programming Models

Exhibit 4-4 A company blends silicon and phosphorous to produce two types of fertilizers.Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound.Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound.The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound. -Refer to Exhibit 4-4.Assuming that all fertilizer produced can be sold,determine the optimal blending plan for the company.What is the maximum profit?

Exhibit 4-1 A hospital emergency room requires different numbers of nurses on different days of the week.The number of full-time employees required each day is given in the table below. Hospital rules require that nurses work four consecutive days,are on call for one day,and then receive two days off.The hospital wants to meet its daily requirements,while minimizing the number of nurses that must be on staff. -Refer to Exhibit 4-1.Suppose the hospital is experiencing a budget crunch and needs to use the nurses' on call day to temporarily staff the emergency room.Use Solver to formulate and solve the hospital's problem.

Aggregate planning models usually relate a beginning value in one period to an ending value from the previous period.

In blending problems,if a quality constraint involves a quotient,then the problem will be nonlinear.

Exhibit 4-4 A company blends silicon and phosphorous to produce two types of fertilizers.Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound.Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound.The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound. -Refer to Exhibit 4-4.Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous.Which should it choose? What would be the resulting impact on profit?

Which of the following statements is a type of constraint that is often required in blending problems?

Problems in which we must determine how to schedule employees to provide adequate service under the same situation each planning period are referred to as:

When a workforce scheduling problems is formulated as an integer programming model,it has:

The results of a sensitivity analysis with a dual objective model can be shown graphically using a:

If X_ij refers to the number of hours employee i works in week j ,then to indicate that the number of working hours of 4 employees in week 3 should not exceed 160 hours,we must have a constraint of the form

Workforce scheduling problems in which the worker schedules continue week to week are:

Integer programming (IP)models are optimization models in which all of the variables must be integers.

Solver does not offer a sensitivity report for models with integer constraints.

In aggregate planning models,we can model backlogging of demand by allowing a month's inventory to be negative.

Exhibit 4-2 A construction company is preparing for a nine-month project,and will need to develop a staffing plan.The company can assign up to 30 of its own full-time employees to the project,and will hire short-term contract employees to make up any shortage in meeting the personnel requirements.Company employees earn $6,000 per month,while short-term contract employees make $8,600/month.Contract employees can be assigned to the project beginning in any month,and their contract period is two months.The number of workers required for the project by month is shown below: -Refer to Exhibit 4-2.Determine the optimal staffing plan for the project.

Exhibit 4-1 A hospital emergency room requires different numbers of nurses on different days of the week.The number of full-time employees required each day is given in the table below. Hospital rules require that nurses work four consecutive days,are on call for one day,and then receive two days off.The hospital wants to meet its daily requirements,while minimizing the number of nurses that must be on staff. -Refer to Exhibit 4-1.Use Solver to formulate and solve the hospital's problem.

In aggregate planning models,the number of workers available influences the possible production levels.

Exhibit 4-1 A hospital emergency room requires different numbers of nurses on different days of the week.The number of full-time employees required each day is given in the table below. Hospital rules require that nurses work four consecutive days,are on call for one day,and then receive two days off.The hospital wants to meet its daily requirements,while minimizing the number of nurses that must be on staff. -Refer to Exhibit 4-1.Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees,and cannot temporarily schedule nurses on their on call days.Determine a schedule that maximizes the number of weekend days off received by the nurses.

Exhibit 4-3 A meat market manager for a large grocery store is preparing a processing plan to stock the shelves with sausage,ground meat,and jerky,which he can prepare from beef,pork and venison.Sausage and ground meat can be made of any mix of the beef,pork and venison,as long at the fat contents are below 15% for sausage and 10% for ground meat.Sausage sells for $5/pound and ground meat sells for $3/pound.Jerky,which sells or $10/pound,is made in a drying process from beef or venison.In the drying process,there is a 50% loss in weight for jerky made from beef (e.g.,one pound of beef yields 0.5 pounds of beef jerky)and a 30% loss in weight for jerky made from venison.The market can sell at most 500 pounds of sausage,1000 pounds of ground meat,and 100 pounds of jerky before their expiration dates.There are currently 1,000 pounds of beef (10% fat content),500 pounds of pork (8% fat content),and 200 pounds of venison (2% fat content)available for processing. -Refer to Exhibit 4-3.Determine the optimal processing plan for the meat market.

If integer constraints are used in a model,Solver uses an algorithm called branch and round to obtain the solution.