Exam 20: 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.Given the information in the optimal tableau,what is the subcontracting cost,in dollars per unit?

What are the assumptions of linear programming? Provide examples of each.

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 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?

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

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

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.

Which of the following statements regarding linear programming is NOT true?

For an "equal" constraint,only points ________ are feasible solutions.

The CZ Jewelry Company produces two products: (1)engagement rings and (2)jeweled watches.The production process for each is similar in that both require a certain number of hours of diamond work and a certain number of labor hours in the gold department.Each ring takes four hours of diamond work and two hours in the gold shop.Each watch requires three hours in diamonds and one hour in the gold department.There are 240 hours of diamond labor available and 100 hours of gold department time available for the next month.Each engagement ring sold yields a profit of $9;each watch produced may be sold for a $10 profit. a.Give a complete formulation of this problem,including a careful definition of your decision variables.Let the first decision variable, (X1),deal with rings,the second decision variable, (X2),with watches,the first constraint with diamonds,and the second constraint with gold. b.Graph the problem fully in the following space.Label the axes carefully,plot the constraints,shade the feasibility region,plot at least one isoprofit line that reveals the optimal solution,circle the corner points and highlight the optimal corner point so found,and solve for it algebraically.(Show all your work to get credit. )

A binding constraint is the amount by which the left-hand side falls short of the right-hand side.

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:

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

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,what is an appropriate constraint for this scenario?

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is correct?

Consider a corner point to a linear programming problem,which lies at the intersection of the following two constraints: 6X1 + 15X2 < 390 2X1 + X2 < 50 Which of the following statements about the corner point is true?

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

A small oil company has a refining budget of $200,000 and would like to determine the optimal production plan for profitability.The following table lists the costs associated with its three products. Marketing has a budget of $50,000,and the company has 750,000 gallons of crude oil available.Each gallon of gasoline contributes 14 cents of profits,heating oil provides 10 cents,and plastic resin 30 cents per unit.The refining process results in a ratio of two units of heating oil for each unit of gasoline produced.This problem has been modeled as a linear programming problem and solved on the computer.The set up and output follows: a.Give a linear programming formulation for this problem.Make the variable definitions and constraints line up with the computer output. b.What product mix maximizes the profit for the company using its limited resources? c.How much plastic resin is produced if profits are maximized? d.Give a full explanation of the meaning of the three numbers listed following. First Number: Slack or surplus of 42500 for the #2 Marketing Budget constraint. Second Number: Shadow price of 0 for the #1 Refining Budget constraint. Third Number: An upper limit of "infinity" for the right-hand-side value for the #1 Refining Budget constraint.

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

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 ounces of tomatoes.Which of the following statements is best?

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 regular output be for month 3?