Explanation Given: Minimize w = 3 y 1 + 2 y 2 + 3 y 3 Subject to: 2 y 1 + 3 y 2 + 6 y 3 ≤ 60 y 1 + 4 y 2 + 5 y 3 ≥ 40 with y 1 ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Explanation: Consider the problem: Minimize w = 3 y 1 + 2 y 2 + 3 y 3 Subject to: 2 y 1 + 3 y 2 + 6 y 3 ≤ 60 y 1 + 4 y 2 + 5 y 3 ≥ 40 with y 1 ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Since this is a nonstandard minimization problem, convert it into a maximization problem by letting z equal to negative of the objective function: z = − w and then find the maximum value of : z = − 3 y 1 − 2 y 2 − 3 y 3 The problem is as follows: Maximize z = − 3 y 1 − 2 y 2 − 3 y 3 Subject to: 2 y 1 + 3 y 2 + 6 y 3 ≤ 60 y 1 + 4 y 2 + 5 y 3 ≥ 40 with y 1 ≥ 0 , y 2 ≥ 0 , y 3 ≥ 0 Now adding slack and surplus variables in to the constraints gives: Maximize z = − 3 y 1 − 2 y 2 − 3 y 3 Subject to: 2 y 1 + 3 y 2 + 6 y 3 + s 1 + 0 s 2 = 60 y 1 + 4 y 2 + 5 y 3 + 0 s 1 − s 2 = 40 3 y 1 + 2 y 2 + 3 y 3 + z = 0 The initial simplex tableau is: y 1 y 2 y 3 s 1 s 2 z [ 2 3 6 1 0 0 60 1 4 5 0 − 1 0 40 3 2 3 0 0 1 0 ] _ The solution is y 1 = 0 , y 2 = 0 , y 3 = 0 , s 1 = 60 , and s 2 = − 40 , since s 2 is negative, solution is not feasible. Since s 2 has a − 1 in row 2 and the positive entry farthest to the left in row 2 is 1 in column 1. Now: min { 60 2 , 40 1 } = min { 30 , 40 } = 30 Since 2 gives the smallest quotient, so 2 becomes the pivot in column 1. Perform row operation to change the other number in the pivot column to 0. R 1 → 1 2 R 1 gives, y 1 y 2 y 3 s 1 s 2 z [ 1 3 2 3 1 2 0 0 30 1 4 5 0 − 1 0 40 3 2 3 0 0 1 0 ] _ R 2 → R 2 + ( − 1 ) R 1 , R 3 → R 3 + ( − 1 ) R 1 gives, y 1 y 2 y 3 s 1 s 2 z [ 1 3 2 3 1 3 0 0 30 0 5 2 2 − 1 2 − 1 0 10 0 − 5 2 − 6 − 3 2 0 1 − 90 ] _ The basic solution is y 1 = 30 , y 2 = 0 , y 3 = 0 , s 1 = 0 , and s 2 = − 10 .Again, s 2 is negative, solution is not feasible. s 1 and s 2 have a − 1 2 , − 1 in row 2, respectively, and the positive entry farthest to the left in row 2 is 5 2 in column 2. Now min { 30 3 2 , 10 5 2 } = min { 20 , 4 } = 4 Since 5 2 gives the smallest quotient, so 5 2 becomes the pivot. Perform row operation to change the other number in the pivot column to 0. R 2 → 2 5 R 2 gives, y 1 y 2 y 3 s 1 s 2 z [ 1 3 2 3 1 3 0 0 30 0 1 4 5 − 1 5 − 2 5 0 4 0 − 5 2 − 6 − 3 2 0 1 − 90 ] _ R 1 → R 1 + ( − 3 2 ) R 2 , R 3 → R 3 + ( 5 2 ) R 2 gives, y 1 y 2 y 3 s 1 s 2 z [ 1 0 9 5 4 5 3 5 0 24 0 1 4 5 − 1 5 − 2 5 0 4 0 0 − 4 − 2 − 1 1 − 80 ] The basic solution is y 1 = 24 , y 2 = 4 , y 3 = 0 , s 1 = 0 , and s 2 = 0 , a feasible solution but not optimal solution because some indicators are negative

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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4. Identify at least two mistakes in Francisco's work. Correct the mistakes and complete the problem by using the second derivative test. 2f 2X 2. Find the relative maximum and relative minimum points of f(x) = 2x3 + 3x² - 3, using the First Derivative Test or the Second Derivative Test. bx+ bx 6x +6x=0 12x- af 24 = 0 x=0 108 -2 5. Identify at least three mistakes in Francisco's work. Then sketch the graph of the function and label the local max and local min. 1. Find the equation of the tangent line to the curve y=x-2x3+x-2 at the point (1.-2). Sketch the araph of y=x42x3+x-2 and the tangent line at (1,-2) y' = 4x-6x y' (1) = 4(1) - 667 - 2 = 4(-2)4127-6(-2) 5-8-19-20 =

۳/۱ R2X2 2) slots per pole per phase = 3/31 B=18060 msl Ka, Sin (1) Kdl Isin ( sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 120*50 5) Synchronous speed, 120 x 50 S1000-950 1000 Copper losses 5kw 50105 Rotor input 5 0.05 loo kw 6) 1 1000rpm اذا ميريد شرح الكتب فقط Look = 7) rotov DC ined sove in peaper PU + 96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 3" 6" Σ=1 (2-1) π X9

Chapter 4 Solutions

Finite Mathematics (11th Edition)

Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 2E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - Prob. 4E Ch. 4.1 - For Exercises 5-8. (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - For Exercises 5-8, (a) determine the number of...Ch. 4.1 - Introduce slack variables as necessary, then...Ch. 4.1 - Introduce slack variables as necessary, then write...

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