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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A) graph the system of inequalities representing the contraints b)find the value of the objetive function at each corner of the graphed region c)use the values in part b to determine the maximum value of the objetive function and the values of x and y at which the maximum occurs
In solving a problem where 100 different products (100 real variables) are produced using just two resources (2 slack variables), then the combination that will yield the optimal profis A. to produce all 100 products if both resources are used to full capacity. B. to produce, at most 2 products. C. none of the choices are correct. D. to produce only one product.
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)
The Z row of a simplex tableau gives: Select one: a. the maximal value a variable can take on and still have all the constraints satisfied. P b. the net profit or loss that will result from introducing one unit of the variable indicated in that column inte solution. C. the gross profit or loss given up by adding one unit of a variable into the solution. d. the number of units of each basic variable that must be removed from the solution if a new variable is ente.
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
2. a) Mathematical model and 1. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Z max = 3x, + 2x2 Cj 3 -M Constraints: S1 A1 RHS X1 X2 V1 X¡ +2x, <6 Xj 2 7 저20, x2 20 X1 3 1 2 1 Aj -M -2 -1 -1 1 1 Zj 3 6+2M 3+M M -M 18-M C;-Zj 0 -4-2M -3-M -M b) Mathematical model and 2. simplex table of a LP problem is given below. Specify the special case in this problem and explain its reason. Cj 1 -M Z max = x +2x2 Constraints: X1 X2 V1 A1 RHS X2 2 1 1 4 X1 +x, 21 Vị -1 1 -1 1 3 x2 <4 2 2 8. Zj 1 저20, x, 20 Cj-Zj -M -2
a) Specify whether the following axioms are true or false. An LP problem is an optimization problem for which we do the following: i. We attempt to optimize a linear function of the decision variables. ii. Each constraint must be a linear equation or linear inequality. i. The values of the decision variables must satisfy some sets of constraints.
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?
Acme Block Company has orders for 80 tons of concrete blocks at three suburban locations as follows: Northwood-25 tons Westwood-45 tons Eastwood-10 tons Acme has two plants, each of which can produce 50 tons per week. Delivery cost per ton from each plant to each suburban location is as follows: Northwood Westwood Eastwood Plant 1 Plant 2 1 24 30 Which one is a correct constraint? A. X11+X12+X13 = 10 OB. X11+X12+X13 ≤ 25 OC X11+X12+X13 = 45 OD. X₁1+X12+X13 ≤ 50 30 40 ہے 40 42
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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

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