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Match the following terms to their definition Feasible region Binding constraint [Choose] [Choose A feasible solution...
4.132 Answer True or False. 1. A linear inequality constraint always defines a convex feasible re...
4.132 Answer True or False. 1. A linear inequality constraint always defines a convex feasible region 2. A linear equality constraint always defines a convex feasible region. 3. A nonlinear equality constraint cannot give a convex feasible region. 4. A function is convex if and only if its Hessian is positive definite everywhere. 5. An optimum design problem is convex if all constraints are linear and the cost function is convex. 6. A convex programming problem always has an optimum...
S- In the optimal table of the simplex for the following linear programming problem x1, x3,...
S- In the optimal table of the simplex for the following linear programming problem x1, x3, are the basic variables. Min Z=-5X1+3X2+X3 X1+X2-X3<=10 X1+X2+X3<=60 What is the range for the first constraint right hand side for which the optimal table remains feasible? a. b. Is it profitable to increase a unit of resource for the 2nd constraint, if each unit of this resource is purchased for $2? What is the value of objective function and decision variables for this problem?...
a. What is the optimal solution in lay terms? What is the optimal value of the...
a. What is the optimal solution
in lay terms? What is the optimal value of the objective
function?
b. Which constraints are binding? Explain.
c. What are the shadow prices of demand for B constraint and
assembly time constraints? Interpret each.
d. If you could change the right-hand side of one constraint by
one unit (either increase or decrease), which one would you choose?
Why? Show all calculations.
e. State and interpret the ranges of optimality for any one of...
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY i...
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 80 x + z ≥ 60 x + y − w ≤ 50 y + z − w ≤ 50...
Assignment 1. Linear Programming Case Study Your instructor will assign a linear programming project for this assignment...
Assignment 1. Linear Programming Case Study Your instructor will assign a linear programming project for this assignment according to the following specifications. It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the...
questions 5 6 7 PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
Solve the following model using linear programming (allow for continuous values and determine the values of...
Solve the following model using linear programming (allow for continuous values and determine the values of the decision variables and objective function. Then, round the decision variables values down to the nearest integer and determine the value of the decision variables and objective function, this is an approximate answer to solving the model using integer programming. Observe if the rounding provides a "feasible solution, all constraints are satisfied. Finally, solve the model using integer programming and determine the values of...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution...
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution exists at a single vertex point. b. There is more than one optimal solution. C. There is no optimal solution because the feasible region does not exist d. There is no optimal solution because the feasible region is unbounded. Maximize: 2x +3y Subject to: x +2y 28 5. Graph the inequality: 2x +3y >12 6. Graph the system of inequalities: 7. Graph the system...
alim Universitesi LMS adi Consider the following linear programming model Maximize z = 3x1 + 2...
alim Universitesi LMS adi Consider the following linear programming model Maximize z = 3x1 + 2 X2 s.t. Xi 54 X1 + 3x2 = 15 2X1 + X2S TO X 30 X220. Calculate the value of the objective function for each of the corner-point (extreme point) solutions. Use this information to identify the optimal solution. Fill the table below with your answers. Extreme-point (x1.x2) Objective Value feasible Z solutions
4.132 Answer True or False. 1. A linear inequality constraint always defines a convex feasible region 2. A linear equality constraint always defines a convex feasible region. 3. A nonlinear equality constraint cannot give a convex feasible region. 4. A function is convex if and only if its Hessian is positive definite everywhere. 5. An optimum design problem is convex if all constraints are linear and the cost function is convex. 6. A convex programming problem always has an optimum...
S- In the optimal table of the simplex for the following linear programming problem x1, x3, are the basic variables. Min Z=-5X1+3X2+X3 X1+X2-X3<=10 X1+X2+X3<=60 What is the range for the first constraint right hand side for which the optimal table remains feasible? a. b. Is it profitable to increase a unit of resource for the 2nd constraint, if each unit of this resource is purchased for $2? What is the value of objective function and decision variables for this problem?...
a. What is the optimal solution
in lay terms? What is the optimal value of the objective
function?
b. Which constraints are binding? Explain.
c. What are the shadow prices of demand for B constraint and
assembly time constraints? Interpret each.
d. If you could change the right-hand side of one constraint by
one unit (either increase or decrease), which one would you choose?
Why? Show all calculations.
e. State and interpret the ranges of optimality for any one of...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
Solve the following model using linear programming (allow for continuous values and determine the values of the decision variables and objective function. Then, round the decision variables values down to the nearest integer and determine the value of the decision variables and objective function, this is an approximate answer to solving the model using integer programming. Observe if the rounding provides a "feasible solution, all constraints are satisfied. Finally, solve the model using integer programming and determine the values of...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
4. Given the following linear programming problem, determine which situation (choose one) a. An optimal solution exists at a single vertex point. b. There is more than one optimal solution. C. There is no optimal solution because the feasible region does not exist d. There is no optimal solution because the feasible region is unbounded. Maximize: 2x +3y Subject to: x +2y 28 5. Graph the inequality: 2x +3y >12 6. Graph the system of inequalities: 7. Graph the system...
alim Universitesi LMS adi Consider the following linear programming model Maximize z = 3x1 + 2 X2 s.t. Xi 54 X1 + 3x2 = 15 2X1 + X2S TO X 30 X220. Calculate the value of the objective function for each of the corner-point (extreme point) solutions. Use this information to identify the optimal solution. Fill the table below with your answers. Extreme-point (x1.x2) Objective Value feasible Z solutions
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