1) Outdoors, Inc. has, as one of its product lines, lawn furniture. They currently have three...

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1) Outdoors, Inc. has, as one of its product lines, lawn furniture. They currently have three items in that line: a lawn chair, a standard bench, and a table. These products are produced in a two-step manufacturing process involving the tube-bending department and the welding department. The time, in hours, required by each item in each department is as follows: Tube bending Welding Lawn Chair 1.2 0.8 Product Bench 1.7 0 Table 1.2 2.3 Present Capacity 1000 1200 The contribution that Outdoors, Inc. receives from the manufacture and sale of one unit of each product is $3 for a chair, $3 for a bench, and $5 for a table. The company is trying to plan its production mix for the current selling season. It feels that it can sell any number it produces, but unfortunately production is further limited by available material, because of a prolonged strike. The company currently has on hand 2000 lbs. of tubing. The three products require the following amounts of this tubing: 2 lbs. per chair, 3 lbs. per bench, and 4.5 lbs. per table. a) (10 points) Formulate the linear programming problem for company, if it tries to maximize its revenue for the current selling season. (Define each variable carefully). b) (4 points) Answer and sensitivity reports, for the above problem, from Excel's Solver are provided below and in the next page (Pay attention to order of constraints in the solution. It may be different then what you had). What is the optimal production mix? What is the corresponding optimal revenue? Solver Options Max Time 100 sec, Iterations 100, Precision 0.000001 Max Subproblems Unlimited, Max Integer Sols Unlimited. Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative Objective Cell (Max) Cell Name Coefficients SES3 Revenue Variable Cells Cell Name $B$2 Values xl SCS2 Values x2 SDS2 Values x3 Constraints Cell Name SES6 Value SES7 Value $E$8 Value Original Value 0 Original Value 0 0 0 Cell Value 1000 866.66667 2000 Final Value 2766.666667 Final Value Integer 700 Contin 0 133.333 Contin Contin Formula Status SES6<=$F$6 Binding Not SES7<-$F$7 Binding SE$8<-$F$8 Binding Slack 0 333.3333 0 Variable Cells Cell Name $B$2 Values x1 $C$2 Values x2 $D$2 Values x3 Constraints Cell Name $E$6 Value $E$7 Value $E$8 Value Final Value 700 0 133.3333 Final Value 1000 866.66667 2000 Reduced Cost 0 -1.383333 0 Shadow Price 1.16667 0 0.8 Objective Allowable Allowable Coefficient Increase Decrease 2 1.38333 1.75 3 3 5 Constraint R.H. Side 1000 1200 2000 Allowable Increase 200 1E+30 555.56 0.7778 1E+30 2 Allowable Decrease 466.67 333.33 333.33 c) (3 points) What is the value of one unit more of tube-bending time? of welding time? pounds of metal tubing? d) (6 points) A local distributor has offered to sell Outdoors, Inc. some additional metal tubing for $0.60/lb. Should Outdoors buy it? If yes, how much would the firm's contribution increase if they bought 500 lbs. and used it in an optimal fashion? e) (6 points) Outdoors, Inc. has a chance to sell some of its capacity in tube bending at cost + $1.50/hour. If it sells 200 hours at that price, how will this affect contribution? f) (6 points) If the contribution on chairs were to decrease to $2.50, what would be the optimal production mix and what contribution would this production plan give? 1) Outdoors, Inc. has, as one of its product lines, lawn furniture. They currently have three items in that line: a lawn chair, a standard bench, and a table. These products are produced in a two-step manufacturing process involving the tube-bending department and the welding department. The time, in hours, required by each item in each department is as follows: Tube bending Welding Lawn Chair 1.2 0.8 Product Bench 1.7 0 Table 1.2 2.3 Present Capacity 1000 1200 The contribution that Outdoors, Inc. receives from the manufacture and sale of one unit of each product is $3 for a chair, $3 for a bench, and $5 for a table. The company is trying to plan its production mix for the current selling season. It feels that it can sell any number it produces, but unfortunately production is further limited by available material, because of a prolonged strike. The company currently has on hand 2000 lbs. of tubing. The three products require the following amounts of this tubing: 2 lbs. per chair, 3 lbs. per bench, and 4.5 lbs. per table. a) (10 points) Formulate the linear programming problem for company, if it tries to maximize its revenue for the current selling season. (Define each variable carefully). b) (4 points) Answer and sensitivity reports, for the above problem, from Excel's Solver are provided below and in the next page (Pay attention to order of constraints in the solution. It may be different then what you had). What is the optimal production mix? What is the corresponding optimal revenue? Solver Options Max Time 100 sec, Iterations 100, Precision 0.000001 Max Subproblems Unlimited, Max Integer Sols Unlimited. Integer Tolerance 5%, Solve Without Integer Constraints, Assume NonNegative Objective Cell (Max) Cell Name Coefficients SES3 Revenue Variable Cells Cell Name $B$2 Values xl SCS2 Values x2 SDS2 Values x3 Constraints Cell Name SES6 Value SES7 Value $E$8 Value Original Value 0 Original Value 0 0 0 Cell Value 1000 866.66667 2000 Final Value 2766.666667 Final Value Integer 700 Contin 0 133.333 Contin Contin Formula Status SES6<=$F$6 Binding Not SES7<-$F$7 Binding SE$8<-$F$8 Binding Slack 0 333.3333 0 Variable Cells Cell Name $B$2 Values x1 $C$2 Values x2 $D$2 Values x3 Constraints Cell Name $E$6 Value $E$7 Value $E$8 Value Final Value 700 0 133.3333 Final Value 1000 866.66667 2000 Reduced Cost 0 -1.383333 0 Shadow Price 1.16667 0 0.8 Objective Allowable Allowable Coefficient Increase Decrease 2 1.38333 1.75 3 3 5 Constraint R.H. Side 1000 1200 2000 Allowable Increase 200 1E+30 555.56 0.7778 1E+30 2 Allowable Decrease 466.67 333.33 333.33 c) (3 points) What is the value of one unit more of tube-bending time? of welding time? pounds of metal tubing? d) (6 points) A local distributor has offered to sell Outdoors, Inc. some additional metal tubing for $0.60/lb. Should Outdoors buy it? If yes, how much would the firm's contribution increase if they bought 500 lbs. and used it in an optimal fashion? e) (6 points) Outdoors, Inc. has a chance to sell some of its capacity in tube bending at cost + $1.50/hour. If it sells 200 hours at that price, how will this affect contribution? f) (6 points) If the contribution on chairs were to decrease to $2.50, what would be the optimal production mix and what contribution would this production plan give?

Answer rating: 100% (QA)

a Formulation of the linear programming problem Let x1 x2 and x3 represent the number of chairs benches and tables produced respectively Objective fun... View the full answer