andX₁ ≥ 0,X₂ ≥ 0.DI (a) Use the graphical method to solve this problem. Circle allthe corner points on the graph.(b) For each CPF solution, identify the pair of constraint bound-ary equations it satisfies.(c) For each CPF solution, identify its adjacent CPF solutions.(d) Calculate Z for each CPF solution. Use this information toidentify an optimal solution.(e) Describe graphically what the simplex method does step bystep to solve the problem. 4.1-2. Consider the following problem.Z = 3x₁ + 2x₂,Maximizesubject to2x₁ + x₂ ≤ 6x₁ + 2x₂ ≤ 6

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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D,I 3.1-5.* Use the graphical method to solve the problem: Maximize Z = 2x₁ + x₂, subject to X₂10
8. Solve the following non-standard maximum value problems. Мах P= 3x + 4x, S.t. * +x, <12 5x, + 2х, 236 7x, +4х, 214 X 20 x, 20
2. Sketch out the possible solution area (shade the area). Label all corner points with an ordered pair (x,y). x+y >1 4x + 3y 0 3. The solution area in problem number 2 represents how to maximize profits for your company. Your boss wants to know ALL the possible ways to maximize profits. a. Tell me one function in the form z= Ax + By, that will produce an infinite number of ways to maximize profits. b. Write a 2 or 3 sentence summary to your boss on why the function will work. Explain it from a mathematical perspective, because your boss also took Math 12.
2 2. (10 pts) Consider the product XY where x and y are positive numbers which 2, must sum to six (6). Find the maximum value of xy under this contraint. a. Write the constraint equation. b. Use the equation in (a) to write the objective function in terms of the variable x. C. Apply the necessary calculus to solve the problem. Be sure to include a verification step, i.e. why your solution is the maximum. Also, give the maximum value.
[3.27] Consider the following problem: Maximize 2x₁ subject to X1 2x1 X1 X1, + x2 + 2x₂ + 3x2 x2, + 6x3 + 4x3 + x3 X3 X3, 11+ + 4x4 ********* X4 X4 ≤6 < 12 2 ≤ X4 X4 2 0.
Maximize z = 4x1 + 17x2, subject to 4x1 + 5x2 ≤ 15 3x1 + X2 ≤ 30 X1 ≥ 0, X2 ≥ 0. X1 X2 $1 52 Z 4 5 1 0 0 15 3 1 0 1 0 30 -4 -17 0 0 1 0
A company produces two products in the amount x andy and the respective prices Px and Px. The two prices are given to be Px = 48-x-y Py = 60 - x - 2y If the unit cost of producing the first product is 8 and that of producing the second is 4, what are the production levels x and y that maximize profit? Prove that profit is indeed maximized.
The profit function of Company ABC for a specific product is given by y = x³ - 6x² +9x and 0≤x≤ 2. Xx Furthermore, let x be the quantity in thousand units and y the profit in hundred thousand pesos. Determine the quantity that gives the maximum profit. O x=1 O x=1.5 O x=1.25 O x=2
3. Determine whether x = T (0 3 0 9 2) is a solution to 3x2 + 2x5 max X1,2,3,4,5 ER subject to x1 + x2x5 x2 + x3 + x5 -2x2 + x4+x5 X1, X2, X3, X4, X5 = = 1 5 5 0 (3)
Sketch the following problem graphically: max f = x2 X2 subject to g1 = X1 – (1 – x2)³ < 0 92 = x1 2 0 Find the solution graphically. Apply the optimality conditions and monotonicity rules. Discuss. (From Kuhn & Tucker, 1951.)
3x2. 22. Solve the following problem for the optimal solution using simplex: minimize 20x, + 10x, + 1-í.x3 subject to xz + 2v, 2 72 *ュー All variables 0 1 2x, + 2xz 2 72 .rz 2 18

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4.1-2. Consider the following problem. Z = 3x₁ + 2x₂, Maximize subject to 2x₁ + x₂ ≤ 6 x₁ + 2x₂ ≤ 6