Q2) Using Graphical Method to determine the optimalvalue of X1 & X2 that maximize value of Z,Max. Z = 5 X1 + 14 X2Subject to;X1 + 3 X2 < 9,3 X1 + X2 < 9,4X1 <8Where X1, X2 > 0

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Answered: Q2) Using Graphical Method to determine…

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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3. The vertex, x-intercepts, y-intercept, and line of symmetry for f(x)= 2.x² +4x – 3 are: -2-V10 -2+ V10 а. У(, -5); ,0 |; (0,-3); x=-1. 2 2.01:(0.): -2-V10 -2+ V10 b. V(-1,-5); ,0 |; (0,3); x=-1. 2 c. V(-1,-5); 2 -2-V10 -2+ V10 ,0 ,0 |; (0,–3); x=-1. 2 -2-V10 -2+y10 d. V(-1,5); ,0 |; (0,–3); x=-1. 2 e. V(-1,-5); -2- V10 -2+ V10 ,0 |; (0,–3); x=1. 2
(2) A retailer determines that the cost of ordering and storing units of a product can be modelled by by C(x) = 3x+ 20000 ,0sxs200, Find the order size that will minimise ordering and storage cost.
1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few weeks. Her sales over the first few weeks of the summer were stacked according to the model S(x) =2x³ – 32x2 + 128x + 6 , where x is the number of weeks and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does this seem reasonable? What kind of conclusions would you make about the weather with this model?
Q1.- a) Consider the following optimization problem: min 5x1 – 6x2 + 4x3 s.t 2x1 +3x2 -x3<-2 -x1 +2x2 +2x3 <3 x1,x2,x3 20 Show graphically that the dual of this problem is unbounded. What does this say about the primal optimization problem?
2. Let f:R – R be the quadratic function defined by f(x) = 3x² – 12x + 15. i) Vertex and Axis of Symmetry of f(x) The maximum or minimum value of f(x) ii) %3D i) Intervals where f(x) is increasing or decreasing. iv) Domain and Range of f(x) v) Draw graph of the function (Show intercepts on the graph)
6. Which of the following is the equation of the quadratic function with f (1) = 0 and f(5) = -6, an axis of symmetry at x =, and a vertex that is a maximum? A f(x) =x- 1)(* - 4) B f(x) = -(x-1)(x – 4) C f(x) = -(x+1)(x + 4) D f(x) =(x+ 1)(x + 4) GO ON TO THE NEXT PAGE. -6- luminate Education TM Inc. acer
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Maximize f = 5x1 - 20x2 subject to -2x1 + 10x2 <= 5, 2x1 + 5x2 <= 10
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Consider the matrices 2 1 4 0 13 1 2 -1 A = |0 3 -6 1 |-1 2 -7 1 4 1 17 -1 7 [1 0 3 7 0 8 25 -3 -19 1 -2 -1 0 0 R = 0 0 0 0 0 0 0 0 1 9 0 0 0 0 1 1 9. and 1 4. -5 2 10 2 1 2 34 You may assume that R is the reduced row-echelon form of A. Let ã1, ...,ā7 E R° denote the columns of A, in left-to-right order. (a) Which of the vectors ā3, ā4, and ās belong to the span of ã1 and ã2? No justification necessary. (b) What is the largest number of linearly independent vectors that can be chosen from among ã1,...,ā7? No justification necessary. (c) Does āz belong to the span of ã1, ã2, and ã4? If not, explain why not; if so, write ãg explicitly as a linear combination of ā1, ā2, and ã4. (d) linear dependence relation among these four vectors (this means an equation of the form Are ā1, ā2, ā6, and ã7 linearly independent? If so, explain why; if not, provide a nontrivial ciải + czã2 + cçãs + c7ã7 = ở
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Q2) Using Graphical Method to determine the optimal value of X1 & X2 that maximize value of Z, Max. Z = 5 X1 + 14 X2 Subject to; X1 + 3 X2 < 9, 3 X1 + X2 < 9, 4X1 <8 Where X1, X2 2 0