When many constraints are present in a linear optimization problem, there is a greater chance that a redundant constraint exists. Assume you are trying to maximize an objective function and you have two decision variables, X1 and X2. If a redundant constraint exists, does the constraint become necessary if you try to minimize (instead of maximize) the same objective function? Why? Do you need an objective function to determine if a constraint is redundant? Explain.
A redundant constraint is that constraint which does not take participation is forming the feasibility region.
In other words, the boundaries of the feasibility region are not formed using this constraint.
This has got nothing to do with the objective. Whether it is minimization or maximization, the feasibility area does not change.
Therefore, the redundancy of a constraint, as it depends only on the feasibility region, cannot also change with the change of objective.
We do not need an objective function to determine if a constraint is redundant.
NOTE:I HOPE YOUR HAPPY WITH MY ANSWER..**PLEASE SUPPORT ME WITH YOUR RATING...THANK YOU.....
When many constraints are present in a linear optimization problem, there is a greater chance that...
Formulate the followings into optimization problems. While you could use the integer constraints, the linear structure should be maintained. However, you shouldn’t use the integer constraints if you can formulate the problem without them. Describe the decision variables, objective function and constraints carefully. You don’t need to solve this problem. (b) (5 pts) A KAIST student is planning a back-pack trip to Europe for this summer. There are 11 items (1 through n) that she is considering to carry to...
Formulate the followings into optimization problems. While you could use the integer constraints, the linear structure should be maintained. However, you shouldn’t use the integer constraints if you can formulate the problem without them. Describe the decision variables, objective function and constraints carefully. You don’t need to solve this problem. (b) (10 pts) Three workers are available to perform two jobs. The timei takes each worker to perform each job is given in the following table. Formulate the problem to...
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...
QUESTION 20 In what parts of a linear programming formulation do the decision variables appear? In the objective function only In the RHS of constraints only In the LHS of constraints only Can appear in both RHS and LHS of constraints AND the objective function None are correct QUESTION 21 A constraint that directly affects the optimal solution in a linear program is called A non-binding constraint A null constraint A binding constraint None of the above QUESTION 22 Which...
Your problem will have exactly two variables (an X1 and an X2) and will incorporate a maximization (either profit or revenue) objective. You will include at least four constraints (not including the X1 ≥ 0 and X2 ≥ 0 [i.e., the “Non-negativity” or “Duh!”] constraints). At least one of these four must be a “≤” constraint, and at least one other must be a “≥” constraint; do not include any “= only” constraints. You must have a unique Optimal Solution...
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 $2? What is the value of objective function and decision variables for this problem?...
Using the information provided below, construct a linear model to maximize the profits for Puck and Pawn Company that produces hockey sticks and chess sets. Product Labor (Hr./Unit) Wood (Lb./Unit) Profit ($/Unit) Hockey Sticks (x1) 1 4 40 Chess Sets (x2) 2 3 50 Resource Availability: 40 hrs of labor per day; 120 lbs of wood Decision Variables: x1 = number of Hockey Sticks to produce; x2 = number of Chess Sets to produce Identify the Objective Function: Z =...
You’ve been asked to develop a problem that can be used to explain some of the concepts you know to someone who has never heard of linear programming. 1. Formulate a maximization problem such that the following conditions are met (you may not use a problem has appeared on this assignment). Make sure to include all elements of formulation that we have discussed (i.e., objective function, constraints, non-negatives). a. LP problem with two decision variables (using X and Y as...
Optimization Problem QUESTION 1 15 Marks A post office requires different numbers of full-time employees on different days of the week. Each full-time employee must work five consecutive days and then receive two days off. In Table 1, the number of employees required on each day of the week is specified. Table 1: Employee work schedule Day 1=Monday 2=Tuesday 3=Wednesday 4=Thursday S=Friday 6=Saturday 7=Sunday Number of full-time Employees Required 17 13 15 19 16 Formulate a linear programming (LP) model...
Styles Problem 15, p. 850 Given this linear programming model, solve the model and then answer the questions t follow Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine 5x1 + 4x2 + 3x3 S 160 minutes Labor 4x1 + 10x2 + 4x3 = 288 hours Materials 2x1 + 2x2 + 4x3 200 pounds Product 2 x2 s 16 units x1, x2, x320 not change 1 If...