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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Description: 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% Ch

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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

π_i≥ 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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