24. In order for a linear programming problem to have a unique solution, thesolution must existA) at the intersection of the non-negativity constraints.B) at the intersection of a non-negativity constraint and a resource constraint.C) at the intersection of the objective function and a constraint.D) at the intersection of two or more constraints.

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Answered: 24. In order for a linear programming…

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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Identify if the given linear programming problem is a standard maximization problem. If it is a standard maximization problem, then express the constraints as slack variable equations, write the objective function in standard form, and set up the initial simplex tableau. If it is not a standard maximization problem, then explain all the reasons why it is not and type NA (or Not Applicable) in the remaining boxes. Maximize: P=100x+240y subject to: 24x+30y≤150 4x+11y≤35 2x-5y≤0 0≤x, 0≤y Standard Max Answer Here, Yes or No with reasons (Keyboard only): Slack Variable Equations Here: (enter NA if it is not a standard maximization problem) Objective Function in Standard Form Here: (enter NA if it is not a standard maximization problem) Initial Simplex Tableau Here: (enter NA if it is not a standard maximization problem)
Identify if the given linear programming problem is a standard maximization problem. If it is a standard maximization problem, then express the constraints as slack variable equations, write the objective function in standard form, and set up the initial simplex tableau. If it is not a standard maximization problem, then explain all the reasons why it is not and type NA (or Not Applicable) in the remaining boxes. Maximize: P=100x+200y+50z subject to: 5x+5y+10z≤1000 10x+5y≤50 0≤x, 0≤y, 0≤z Standard Max Answer Here, Yes or No with reasons (Keyboard only): Slack Variable Equations Here: (enter NA if it is not a standard maximization problem) Objective Function in Standard Form Here: (enter NA if it is not a standard maximization problem) Initial Simplex Tableau Here: (enter NA if it is not a standard maximization problem)
Prepare a graph of the constraints and objective function and solve the following linear programming problem: Maximize: f=2x₁-x₂ Subject to constraint 1: x₁ + x₂ ≥ 2 constraint 2: x₁ + x₂ ≤5 constraint 3: x₁-x₂ ≤1 constraint 4: -x₁ + x₂ ≤4 constraint 5: x, 20 constraint 6: x₂ 20 Hints: Draw the line of each constraint on the graph below (two constraints are already drawn) After drawing all the lines shade the optimal region. Try f-0, f=2 and f-4. Which one is the optimum, and what are the values of x1 and x₂? -B constraint2 -2 -1 -5 --4- 3- 2- 1 +0 -1- -2 -3- -4 X₂ 0 constraint4 1 2 3 4 5 X 6 X₁
1. Set up a linear programming model of the situation described. Determine whether it is in standard form. If not make it standard. A restaurant chef is planning a meal consisting of two foods, A, and B. • Each kg of A contains 3 units of fat and 6 units of protein • Each kg of B contains 1 unit of fat and 3 units of protein The chef wants the meal to consist of at least 18 units of protein and at most 6 units of fat. If the profit that he makes is 3 dollars per kg for food A and 5 dollars for food B, how many kilograms of each food should be served so as to maximize his profit?
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1. Show how the nonconvex shaded solution spaces in the figures below can be represented by a set of simultaneous constraints. (Hint: use either or constraints) x₂ 2 1 0 1 2 3 X1 3 2 1 012 3 (b) 3 2 1 012 3 X₁
Solve the following linear programming problem. z = 2x + 7y 5x + 4y ≤ 20 8x + y ≤ 20 x ≥ 0, y 20 Maximize: subject to: The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)

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