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(a) A stationary supplies company wishes to produce deluxe and budget ink pens. Deluxe ink pens require eight units of material and 9 minutes to produce each pen. Budget ink pens require six units of material and 4 minutes to produce each pen. The company has 38.25 hours of labour and 1950 units of material available per week. Profit for deluxe ink pens is $2.40 per pen and for budget ink pens is $1.75 per pen. The company also wants the number of deluxe ink pens to be produced to be at least 6 times the number of budget ink pens produced. Formulate a Linear Programming problem to determine the company's best production plan to maximise profit (do not solve). (b) Solve the following Linear Programming problem using the Simplex Method. Full working by hand must be shown. From the following tableau determine the current solution to the linear programming problem and its type. Explain your reasoning. CB 4 0 C₂ XB X3 21 82 Zj Zj-Cj 9 x1 0 1 0 9 0 15 X2 0 3 4 27 12 4 x3 1 0 0 4 0 0 81 -1 5 1 41 41 0 82 0 1 0 0 0 83 -2 2 10 10 b 42 2 -13 186

(a) A stationary supplies company wishes to produce deluxe and budget ink pens. Deluxe ink pens require eight units of material and 9 minutes to produce each pen. Budget ink pens require six units of material and 4 minutes to produce each pen. The company has 38.25 hours of labour and 1950 units of material available per week. Profit for deluxe ink pens is $2.40 per pen and for budget ink pens is $1.75 per pen. The company also wants the number of deluxe ink pens to be produced to be at least 6 times the number of budget ink pens produced. Formulate a Linear Programming problem to determine the company's best production plan to maximise profit (do not solve). (b) Solve the following Linear Programming problem using the Simplex Method. Full working by hand must be shown. From the following tableau determine the current solution to the linear programming problem and its type. Explain your reasoning. CB 4 0 C₂ XB X3 21 82 Zj Zj-Cj 9 x1 0 1 0 9 0 15 X2 0 3 4 27 12 4 x3 1 0 0 4 0 0 81 -1 5 1 41 41 0 82 0 1 0 0 0 83 -2 2 10 10 b 42 2 -13 186

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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apply appropriate techniques to solve a range of models of mathematical and real-world problems analyse the effects of changing model parameters on LP model predictions * select and develop appropriate mathematical models for decision making problems (a) A stationary supplies company wishes to produce deluxe and budget ink pens. Deluxe ink pens require eight units of material and 9 minutes to produce each pen. Budget ink pens require six units of material and 4 minutes to produce each pen. The company has 38.25 hours of labour and 1950 units of material available per week. Profit for deluxe ink pens is $2.40 per pen and for budget ink pens is $1.75 per pen. The company also wants the number of deluxe ink pens to be produced to be at least 6 times the number of budget ink pens produced. Formulate a Linear Programming problem to determine the company's best production plan to maximise profit (do not solve). (b) Solve the following Linear Programming problem using the Simplex Method. Full working by hand must be shown. From the following tableau determine the current solution to the linear programming problem and its type. Explain your reasoning. CB 4 9 0 Cj XB x3 21 82 Zj Zj - Cj 9 x1 0 1 0 9 0 15 I2 0 3 4 27 12 4 x3 1 0 0 4 0 0 $1 -1 5 1 41 41 0 82 0 0 1 0 0 0 83 -2 2 4 10 10 b 42 2 -13 186
Transcribed Image Text:apply appropriate techniques to solve a range of models of mathematical and real-world problems analyse the effects of changing model parameters on LP model predictions * select and develop appropriate mathematical models for decision making problems (a) A stationary supplies company wishes to produce deluxe and budget ink pens. Deluxe ink pens require eight units of material and 9 minutes to produce each pen. Budget ink pens require six units of material and 4 minutes to produce each pen. The company has 38.25 hours of labour and 1950 units of material available per week. Profit for deluxe ink pens is $2.40 per pen and for budget ink pens is $1.75 per pen. The company also wants the number of deluxe ink pens to be produced to be at least 6 times the number of budget ink pens produced. Formulate a Linear Programming problem to determine the company's best production plan to maximise profit (do not solve). (b) Solve the following Linear Programming problem using the Simplex Method. Full working by hand must be shown. From the following tableau determine the current solution to the linear programming problem and its type. Explain your reasoning. CB 4 9 0 Cj XB x3 21 82 Zj Zj - Cj 9 x1 0 1 0 9 0 15 I2 0 3 4 27 12 4 x3 1 0 0 4 0 0 $1 -1 5 1 41 41 0 82 0 0 1 0 0 0 83 -2 2 4 10 10 b 42 2 -13 186
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