Consider the following LP: Max Z = x1 + x2 s.t. X1 + x2 < 3 X1 – 2x2 >0 X1, X2 2 0 a. Solve the problem graphically: clearly mark each constraint, the feasible region, the iso-profit line and the optimal solution on the graph.
Q: Construct one example for each of the following types of two-variable linear programs. •Infeasible.…
A: Below is the solution:-
Q: Solve using the duality linear programming method of the following problem: Object Function: F =…
A:
Q: . Solve the following linear programming model graphically: minimize Z = 3x, + 6x2 kubject to 3x +…
A: A way of optimizing operations with some constraints is linear programming. Linear programming's…
Q: Solve the following linear programming problem using the graphical method and answer the following…
A: Note: Since you have posted a question with multiple subparts, we will solve the first three…
Q: Given the following output for the optimal solution for a 4 variable (named BR, IC, COLA, and PC)…
A: Summary: In the given details, results show how much the objective coefficient may…
Q: Solve the following LP problem. Note that in this LP problem, the constraint functions are the same…
A: THE ANSWER IS AS BELOW:
Q: Solve the following Linear programming problem using the simplex method:Maximize Z = 10X1 + 15X2 +…
A: Given MAX Z = 5x1 + 10x2 + 8x3subject to3x1 + 5x2 + 2x3 <= 604x1 + 4x2 + 4x3 <= 72and x1,x2,x3…
Q: What is the special case that is associated with the following Linear ?Programming problem Max Z=…
A: Linear programming is nothing but the simple approach where an individual can represent complex…
Q: Minimize Z = -4x1 + x2 Subject to 8x1 + 2x2 =>16 4x1 + 2x2 =0 Identify the feasible solution area…
A:
Q: Solve the following Linear programming problem using the simplex method: Maximize Z = 10X1 + 15X2 +…
A: We will answer the first question since the exact one wasn't specified. please submit a new question…
Q: Consider the following LP problem with two constraints: 32X + 39Y >= 1248 and 17X + 24Y >= 408. The…
A:
Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…
A: The initial tableau can be written as follows.
Q: The LP problem is given by, Maximize profit 8X1+ 5X 2 Subject to: X1+X2s 10 X1s6 X1 0 X220 Use…
A: Linear programming is a technique to reach the best outcome like maximum profit or lowest cost whose…
Q: Given the following 2 constraints, which solution is a feasible solution for a minimization problem?…
A: The points x1 and x2 become feasible when they satisfy both constraints.
Q: What is Optimization? How many methods are there to calculate it? Explain this?
A: Hello thank you for the question. As per guidelines, we would provide only one answer at a time.…
Q: suppose a linear programming (maximation) problem has been solved and that the optimal value of the…
A: This might affect the optimal value of the objective function as follows
Q: Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)…
A: Here, It is LP problem that I need to solve, It is part of Operations Management LP problem is as…
Q: Min 4x1 + 6x2 s.t 2x1 + 2x2 ≥ 3, x1 + 3x2 ≥ 2, x1 +…
A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…
Q: Find the optimal solution for the following problem. (Round your answers to 3 decimal places.)…
A: Here, It is part of Operations Management question, LP problem is as stated below: MAXIMIZE: Z = 14…
Q: 2.1) On the solution graph, use a dashed line to demonstrate how the optimal solution is to be…
A: Below is the solution:-
Q: Solve using the duality linear programming method of the following problem: Object Function: F =…
A:
Q: Problem 2 Consider the following problem: max 2x1 + 72 + 4x3 s.t. x1 + 2x2 +x3 0. Use the dual of…
A: given,
Q: A linear programming problem is given as follows: max Z=−4x1+ x2 Subject to 8x1+2x2≥16 4x1+2x2≥12…
A: Objective Functions and Constraints: Based on the given details, the objective…
Q: Solve the following linear programming problem using the graphical method and answer the following…
A:
Q: Suppose a linear program graph results in a number line for the binding constraints as follows: -3…
A: Give, Objective function- Max 5X1 + 10X2
Q: Consider the following set of constraints: 48Y >= 7296; 0.25 X + 12Y >= 1824, and X + Y <= 152. Pick…
A:
Q: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty…
A:
Q: Given this linear programming model, solve the model and then answer the questions that follow.…
A: Note: Since you have posted a question with multiple subparts, we will solve the first three…
Q: A linear programming problem is given as follows: min Z = −4x1 + x2 Subject to 8x1 + 2x2 ≥ 16 4x1 +…
A:
Q: Solve the following problem using graphical linear programming.Minimize Z = 8x1 + 12x2 Subject to…
A: The feasible region for the problem moves away from the encompassing the points shown above.…
Q: Solve the linear programming problem by the simplex method. Maximize 40x+ 30y subject to the…
A: Objective function: Max Z = 40x+30y Constraints: x+y≤8-2x+3y≥15x≥0, y≥0
Q: x1 + x2 ≤30 300 ≤5x1 + 6x2 x1 ≥0, x2 ≥0. From the given constraint above, provide the following a.…
A: Linear programming is a mathematical technique that is also used in operations management…
Q: 2.1) On the solution graph, use a dashed line to demonstrate how the optimal solution is to be…
A: Below is the solution:-
Q: Simplify the following problem minimize 35x, + 7x2 + 10x3 + 3x, + x5 subject to x1 - 3x2 + x3 + x, -…
A: Given Information: Minimize Z: 35x1 + 7x2 + 10x3 + 3x4 + x5 Subject to constraints: x1 - 3x2 + x3 +…
Q: The problem below involves three variables. Solve it with the simplex method, Excel, or some other…
A: Let, A = Units of Aries to be built B = Units of Belfair to be built W = Units of Wexford to be…
Q: Solve using the simplex method the following problem: Maximize Z=3X1 + 2X2 subject to: 2X1+ X2 ≤ 18…
A: Problem is Max Z = 3 x1 + 2 x2 subject to 2 x1 + x2…
Q: Solve the following LP problem Maximize Z(x1,x2) = 3x1 + 2x2 Subject to 2x1 + x2 < 12 - x1+ x2 < 3…
A: Below is the solution:-
Q: Consider the following network representation of a transportation problem: Des Moines 475 266…
A: Network representation procuring intends to implant the vertexes in an organization into…
Q: Consider the following linear programming problem: Maximize 4X + 10Y Subject to:…
A: THE ANSWER IS AS BELOW:
Q: Maximize Z = 2x1 + 5x2 + 3x3 subject to 2x2 + 2x1 + 4x2 + Т1> 0, 22 2 0, Хз > 0. (1) (2) X1 X3 > 20…
A: given,
Q: Consider the following LP model in standard form, with a row for the objective function Z. a) Put it…
A: Tableau FormThe variables x3, x4 and x5 are having negative coefficients and hence they will get a…
Q: 1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to…
A:
Q: Problem 4: Use the big-M method to solve the following linear program. 2x1 +2x2 +4x3 +4x2 +2x3 <4…
A: Big-M or Simplex method : The Big M technique is a simplex algorithm-based solution for tackling…
Q: Consider the following linear programming problem: Maximize: 12X + 10Y Subject to: 4X +3Y ≤ 480 2X…
A: Max z = 12x + 10y subject to 4x + 3y≤ 480 2x + 3y ≤360 x,y≥ 0
Q: 2. Solve the following problem using graphical method. Show all the feasible solutions and obtain…
A: Given data, Min Z = 2x1 + 9x2 Subject to constraints 2x1 + 2x2≥15 0x1 +4x2 ≤45 0x2 + 3x2 ≤80…
Q: Suppose the price of a BR increases from 50 to 60 and the price of a PC decreases from 80 to 50.…
A: The reduced costs tell us how much the objective coefficients (price) can be increased or decreased…
Q: Consider the following LP problem. Minimire 2- 9.20x, + 5.90x2 Subject toi Constraint 1 Sx1 + 3x2…
A: a.
Q: Consider the following linear program: Maximize 30X1 + 10X, Subject to: 3X +X, < 300 X +X, s200 X1s…
A:
Q: Find the optimal solution for the following problem. Maximize C = 4x + 12y subject to 3x +…
A: Formula:
Q: Construct one example for each of the following types of two-variable linear programs. •Feasible…
A: Objective Function: Maximize Z = 123 X + 138 Y Decision Variables: X…
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
- Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…Consider the following linear programming model with 4 regular constraints:Maximize 3X + 5Y (a) Draw your graph in the space below:subject to: 4X + 4Y ≤ 48 (constraint #1) 4X + 3Y ≤ 50 (constraint #2) 2X + 1Y ≤ 20 (constraint #3) X ≥ 2 (constraint #4) X, Y ≥ 0 (non-negativity constraints)(a) Which of the constraints is redundant? Constraint #______.Justify by drawing a graph similar to Figure 7.14 on p.263.(b) Is point (9,3) a feasible solution? _____. Explain your answer (by analyzing each of the constraints).Constraint #1: _______________________________________________________________Constraint #2: _______________________________________________________________Constraint #3: _______________________________________________________________Constraint #4: ______________________________________________________________Draw a graph that identifies the feasible region for the following set of constraints. 0.25 A + 0.25 B ≥ 30 0.5 A + 5 B ≥ 200 0.75 A + 1.5 B ≤ 150 A, B ≥ 0
- 1. Consider the following linear programming formulation: Min 5x + 2y Subject to (1) 3x + 6y ≥ 18 (2) 5x + 4y ≥ 20 (3) 8x + 2y ≥ 16 (4) 7x + 6y ≤ 42 (5) x, y ≥ 0 a. Solve the problem graphically. Specifically, show each constraint and the feasible region, draw an objective function line and identify an optimal point (the solution). When reporting the optimal solution and the corresponding objective function value, you may estimate the optimal x and y values from the graph. b. What are the optimal values of x and y, using the solver add-in? What is the corresponding value of the objective function? c. How many extreme points does the feasible region have? Enumerate them. Hint: It's from the graph. d. Change the objective function to 15x + 12y.. What is the new optimal solution(s)?Given the following 2 constraints, which solution is a feasible solution for a minimization problem? (1) 7 x1 + 3 x2 ≥ 21 (2) x1 + 3 x2 ≥ 6 Group of answer choices (x1, x2) = (2, 5) (x1, x2) = (1, 2) (x1, x2) = (0, 4) (x1, x2) = (0.5, 5)Set up the simplex matrix used to solve the linear programming problem. Assume all variables are nonnegative.Maximize f = 5x + 9y subject to 8x + 5y ≤ 200 x + 6y ≤ 250. x y s1 s2 f first constraint second constraint objective function
- A linear programming problem is given as follows:max Z=−4x1+ x2 Subject to 8x1+2x2≥16 4x1+2x2≥12 x1≤5 x2≥3 x1,x2≥0 I) Identify the feasible solution area graphically on the following plot (by shading the area). II) What is the solution of the optimization problem? x1=? x2=? z=?Find the optimal solution for the following problem. (Round your answers to 3 decimal places.) Minimize C = 14x + 7y + 8z subject to 6x + 12y + 19z ≥ 64 17x + 24y + 9z ≥ 128 and x ≥ 0, y ≥ 0, z ≥ 0. What is the optimal value of x? What is the optimal value of y? What is the optimal value of z? What is the minimum value of the objective function?Suppose Jack like to solve the following formulation in Excel. And the problem is setup in Excel like this: See attached picture. A B C D E 1 X1 X2 2 decision variable objective 3 coefficient of objective function 2 3 4 Constraints LHS RHS 5 Constraints 1 2 1 3 6 Constraints 2 4 5 20 7 Constraints 3 2 8 16 8 Constraints 4 5 6 60 We want to put our objective function in cell D3. What should we type in D3? In cell D5 to D8, we will put the left hand side of our constraint. What should we type in D8? In OpenSolver, what should we assign to Variable Cell? What should you do to input the non-negativity constraint in OpenSolver?
- Consider the following constraints from a two-variable Linear Program. (1) X ≥ 0 (2) Y ≥ 0 (3) 5X + 4Y ≤ 50 (4) 5X - 2Y ≤ 20 If constraints (3) and (4) are binding, what is the optimal solution (X, Y)? Answer choices (6, 5) (9, 5) (0, 20) (20, 0)Consider the following LP problem with two constraints: 18X + 8Y >= 144and 9X + 4Y= 36. The objective function is Min 14X + 30Y . What combination of X and Y will yield the optimum solution for this problem? a. infeasible problem b. unbounded problem c. 0 , 9 d. 4 , 0 e. 2 , 4.5Given the following linear program: Max 3x1 + 4x2 s.t. 2x1 + 3x2 < 24 3x1 + x2 < 21 x1, x2 > 0 Identify the feasible region. Find all the extreme points – list the value of x1 and x2 at each extreme point. What is the optimal solution?