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A drug company manufactures two kinds of sleeping pill: Pill 1 and Pill 2. The pills contain a mixture of two different chemicals, A and B (and no other ingredients). Pill 1 must contain at least 65% Chemical A and Pill 2 must contain at least 55% Chemical A. There are two different ways to produce Chemicals A and B. Operating Process P requires 7 Kgs of A raw material to run for one hour and 2 hours of labor time (because it must be supervised by 2 workers). Operating Process Q requires 5 Kgs of A raw material to run for one hour and 3 hours of labor time. Operating Process P produces three Kgs of each chemical for one hour runtime. Operating Process Q produces 3 Kgs of Chemical A and one Kg of Chemical B for one hour runtime. There are L > 0 hours of labor and R > 0 Kgs of raw material available. The company earns A profit from Pill i of πi ≥ 0 (i = 1,2) Kshs per Kg. The company wishes to find a production plan that maximizes the profit it makes from manufacturing sleeping pills. Formulate the problem as a linear programming problem.   Do not solve the resulting linear programming problem.                                                                                                                              Use the two-phase method to solve the following LPP.                                                                              Maximize    :     y = 5x1 + 8x2  Subject to: 3x1 + 2x2 ≥ 3         x1 + 4x2 ≥ 4                              x1 + x2 ≤ 5

A drug company manufactures two kinds of sleeping pill: Pill 1 and Pill 2. The pills contain a mixture of two different chemicals, A and B (and no other ingredients). Pill 1 must contain at least 65% Chemical A and Pill 2 must contain at least 55% Chemical A. There are two different ways to produce Chemicals A and B. Operating Process P requires 7 Kgs of A raw material to run for one hour and 2 hours of labor time (because it must be supervised by 2 workers). Operating Process Q requires 5 Kgs of A raw material to run for one hour and 3 hours of labor time. Operating Process P produces three Kgs of each chemical for one hour runtime. Operating Process Q produces 3 Kgs of Chemical A and one Kg of Chemical B for one hour runtime. There are L > 0 hours of labor and R > 0 Kgs of raw material available. The company earns A profit from Pill i of πi ≥ 0 (i = 1,2) Kshs per Kg. The company wishes to find a production plan that maximizes the profit it makes from manufacturing sleeping pills. Formulate the problem as a linear programming problem.   Do not solve the resulting linear programming problem.                                                                                                                              Use the two-phase method to solve the following LPP.                                                                              Maximize    :     y = 5x1 + 8x2  Subject to: 3x1 + 2x2 ≥ 3         x1 + 4x2 ≥ 4                              x1 + x2 ≤ 5

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CT: Test
Problem 24CT
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  • A drug company manufactures two kinds of sleeping pill: Pill 1 and Pill 2. The pills contain a mixture of two different chemicals, A and B (and no other ingredients). Pill 1 must contain at least 65% Chemical A and Pill 2 must contain at least 55% Chemical A. There are two different ways to produce Chemicals A and B. Operating Process P requires 7 Kgs of A raw material to run for one hour and 2 hours of labor time (because it must be supervised by 2 workers). Operating Process Q requires 5 Kgs of A raw material to run for one hour and 3 hours of labor time. Operating Process P produces three Kgs of each chemical for one hour runtime. Operating Process Q produces 3 Kgs of Chemical A and one Kg of Chemical B for one hour runtime. There are L > 0 hours of labor and

R > 0 Kgs of raw material available. The company earns A profit from Pill i of

πi ≥ 0 (i = 1,2) Kshs per Kg. The company wishes to find a production plan that maximizes the profit it makes from manufacturing sleeping pills. Formulate the problem as a linear programming problem.   Do not solve the resulting linear programming problem.

                                                                                                                    

  •  
 
   

  • Use the two-phase method to solve the following LPP.

                                                                             Maximize    :     y = 5x1 + 8x2

 Subject to: 3x1 + 2x2 ≥ 3

        x1 + 4x2 ≥ 4

                             x1 + x2 ≤ 5

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