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 demand forecast for quarter 2?

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

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

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

The ________ problem is a one-period type of aggregate planning problem,the solution of which yields optimal output quantities of a group of products or services,subject to resource capacity and market demand conditions.

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.

Which of the following statements regarding linear programming is BEST?

________ is an assumption that the decision variables must be either positive or zero.

D.5 The Transportation Method Table D.1 Tanfastic,Inc. ,a manufacturer of swimwear,is in the process of developing a production plan for the coming spring break.The ending inventory for January is 30 units.Undertime is paid,at a rate of $5.00 per unit.Details are shown in the following POM for Windows table. -Use the information in Table D.1.Given the information in the optimal tableau,what is the inventory carrying cost,in dollars per unit per quarter?

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

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?

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

A manager is interested in using linear programming to analyze production for the ensuing week.She knows that it will take exactly 1.5 hours to run a batch of product A and that this batch will consume two tons of sugar.This is an example of the linear programming assumption of:

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

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that:

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 level plan strategy for the six-month planning period.What is the cost for month 6 of their level plan?

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.If the plant has no limits on the number of units produced by overtime or subcontractors,what is the lowest-cost chase plan that is possible for the six-month period?

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.If the planner decides to adopt a chase plan for the planning period,what will the regular output be for month 1?

The ________ represents all permissible combinations of the decision variables in a linear programming model.

Parameters that are quantified without doubt meet the linear programming assumption of ________.