Linear Prog COP4355_Part_56

Linear Prog COP4355_Part_56 - Appendix A: Review of...

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228 Appendix A: Review of Mathematical Tools Appendix A: Review of Mathematical Tools SYSTEMS OF LINEAR EQUATIONS A.1 (a) 2X + 4Y = 14 (b) Y = 14 – 2X 4X + 2Y = 16 Y = -11 + 3X 2X = 14 – 4Y 14 – 2X = -11 + 3X X = 7 – 2Y -5X = -25 4(7 – 2Y) + 2Y = 16 X = 5 28 – 8Y + 2Y = 16 - 6Y = -12 Y = 14 – 2(5) Y = 2 Y = 4 2X + 4(2) = 14 2X = 6 X = 3 (c) 2 = -X + 2Y (d) X + 4Y = -8 35 = 5X - Y 3X + Y = 9 5(2) = 5(-X) + 5(2Y) (-4)(3X) + (-4)(Y) = (-4)(9) 10 = -5X + 10Y -12X - 4Y = -36 35 = 5X - Y X + 4Y = -8 ____________________ _______________________ 45 = 0X + 9Y -11X = -44 Y = 5 X = 4 2 = -X + 2(5) 4 + 4Y = -8 2 = -X + 10 4Y = -12 -8 = -X Y = -3 X = 8 (e) Y = 4X - 13 X = 3Y - 16 Y = 4(3Y – 16) – 13 -11Y = -77 Y = 7 X = 3(7) – 16 = 5
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Solutions Manual and Workbook 229 A.1 (continued) (f) X + Y = 3 2 3X - 2Y = 7 4 X + Y = 6 3X -2Y = 28 3X + 3Y = 18 3X - 2Y = 28 -3X - 3Y = -18 3X - 2Y = 28 - 5Y = 10 Y = -2 X = 6 - (-2) X = 8 A.2 Total investment in A and B is $5,000. (See Graph Below) A + B = 5,000 Return is to be 10% .09A + .12B = .1(5,000) Solving the investment equation for B and substituting into the Return Equation; B = 5,000 – A .09A + .12(5,000 – A) = .1(5,000) .09A + 600 - .12A = 500 100 = .03A A = $3,333 B = 5,000 – A = 5,000 – 3,333 B = $1,667
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230 Appendix A: Review of Mathematical Tools A.3
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Linear Prog COP4355_Part_56 - Appendix A: Review of...

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