Exam 20: Linear Programming

A parameter is a region that represents all permissible combinations of the decision variables in a linear programming model.

Table D.4 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.4.The plant has no limits on the number of units produced by overtime or subcontractors and adopts a level plan strategy for the six-month planning period.What is the cost for month 6 of their level plan?

Belsky Manufacturing makes three models of fans,identified by the unimaginative names of A,B,and C.The fans are made out of nuts,bolts,wire,blades,and motors.The current inventory levels and parts list for each type of fan is shown in the table. Fan A sells for $18,Fan B sells for $25,and Fan C sells for $30. Milo Belsky decided to arrive at an optimal production quantity using linear programming.His initial solution was to produce 50 Fan As and 21.4 Fan Cs for a profit of $1542.86. Determine what his inventory would be. Charlie Belsky made an important change to the model and ran the linear programming software again,His solution was to produce 50 Fan As,-150 Fan Bs,and 150 Fan Cs for a profit of $1650 units.What change did he make to the model and what would the ending inventory be if they were to produce according to this plan? What are the practical implications of this solution?

Degeneracy occurs when the linear program model consists of only an infeasible region.

________ are the limitations that restrict the permissible choices for the decision variables.

A(n)________ is the marginal improvement in the objective function value caused by relaxing a constraint by one unit.

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

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.

What does the feasible region represent?

The ________ is an expression in linear programming models that states mathematically what is being maximized or minimized.

________ represent choices the decision maker can control.

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.

What are some potential abuses or misuses of linear programming (beyond violation of basic assumptions)?

The objective function Maximize Z = 3x2 + 4y is appropriate for linear programming.

Each coefficient or given constant is known by the decision maker with ________.

What is the meaning of a slack or surplus variable?

Only corner points should be considered for the optimal solution to a linear programming problem.

________ occurs in a linear programming problem when the number of nonzero variables in the optimal solution is fewer than the number of constraints.

Table D.4 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.4.If the planner decides to adopt a level plan for the planning period,what will the total output be for month 3?

A manufacturer builds finished items A,B,and C from five different components.They currently have several finished units,a number of items that are partially complete,and many components that have just been delivered from their suppliers.The finished items,incomplete items and raw components can all be assigned some monetary value even though the manufacturer typically does not sell anything except finished items.The manufacturer needs to raise capital quickly so they formulate a linear program to help them decide on the most profitable way ahead.Their linear programming expert forgets to restrict their decision variables to non-negative values and is surprised when the computer output tells them that finished item A and C should be negative? If the company always follows the advice of their linear programming analysis,what should they do and why?