Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decisionvariables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values andranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Roundyour answers to 2 decimal places.

This linear programming (LP) problem aims to minimize the value of a function (z) considering…

Answered: Consider the following LP problem.…

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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Solve the following LP using the simplex method: Note: The constraint with the "=" sign in the simplex iteration is added with an artificial variable, so that it becomes 3x1 + x2 + A1= 3
Q5) Solve the following linear programming by using simplex method: Max Z=4X1 + 5X2 Subject to: X1 + X2 < 10 3X1 + 7X2 < 42 X1, X2 20
Iron Sports is a company that produces exercise equipment. Two of their products, boxing bags and yoga mats have become very popular in recent weeks. In any week, the production depends on a number of constraints. Let x= the number of boxing bags. Let y = the number of yoga mats. Some of the constraints are written below. Constraint 1: The total number of boxing bags and yoga mats that can be produced is less than 50: x + y < 50 Constraint 2: The number of boxing bags that can be produced is less than 40: x< 40 Constraint 3: The total number of boxing bags and yoga mats that can be produced is greater than 30. Constraint 4: The number of yoga mats that can be produced is less than 25. (a) (i) The inequation for constraint 3 can be written as 230. (ii) The inequation for constraint 4 can be written as <25. All constraints are shown on the graph below. y 50
Group B 10 Money manager Boris Milkem deals with French currency (the franc) and American currency (the dollar). At 12 midnight, he can buy francs by paying .25 dollars per franc and dollars by paying 3 francs per dollar. Let x, = number of dollars bought (by paying francs) and x2 = number of francs bought (by paying dollars). Assume that both types of transactions take place simultaneously, and the only constraint is that at 12:01 A.M. Boris must have a nonnegative number of francs and dollars. a Formulate an LP that enables Boris to maximize the number of dollars he has after all transactions are completed. b Graphically solve the LP and comment on the answer.
construct the initial plus one simplex tableaux for the following LPP: Max 5x1+ 6x2 + 6x3 Constraints: x1<= 400 x2 <= 200 x3 <= 100 2x1 + 3x2 + 7x3 <= 1000 1x1 + 1x3 <= 400 3x1 + 5x2 + 10x3 <= 2000 -2x1+x2<= 0 2x1 + 4x2 + 6x3 <= 10000 x1, x2, x3 >= 0
A company produces two types of drills, a cordless model and a corded model. The cordless model requires 3 hours, and the corded-type drill requires 1 hours to make. The company has 180 work hours per day for manufacturing. The factory has space for storage of 140 drills per day. Let z = the number of cordless drills produced per day and y = the number of corded drills produced per day. Write the system of inequalities for these constraints: Assembly: 3x + y Storage: x+y 250+ 240 230- 220- 210- 200 Graph the feasible region for this system of inequalities. Note: To get the correct feasible region, you need to also include the non-negative constraints on your graph (≥0 and y ≥ 0). These will give you boundary lines on the x-axis and y-axis. 190 180 170- 160- 150 140 130 120 110- 100 90- 688888888 80 70 60- 50- 40- 30 20- 10 <180 <140 Clear All Draw: 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250
5
1- Convert the following constraints and objective function into the standard form for use in the simplex: Max Profit: 40X, + 20X₂ Sto 2X; +3X2 ≤ 120 X₁ +2X₂ ≥100 X₁, X₂ 20
Find the minimum and maximum values of z= 3x + 5y, if possible, for the following set of constraints. 4x+3y ≥ 12 x + 3y ≥6 x20, y20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The minimum value is (Round to the nearest tenth as needed.) OB. There is no minimum value.
Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is used to eliminate x rather than y.
2. Consider the following set of constraints: X, + 2x, + 2x, + 4x, < 40 2x, - x, + x, + 2x, < 8 4x, – 2x, + x, – x,< 10 4. Using the Simplex Method, solve the problem for each of the following objective functions. а. Маximize z 3 Зх, — х, + 3x, + 4x, b. Minimize z %3D 5х, - 4х, + 6х, — 8х,
Consider the following minimum problem: Minimize: C= 2x1 +10x2 + 8x3 Subject to the constraints: X2+2x3 2 8 -X1+2x2 +2x3 2 4* |지 20 x2 20 x3 20 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) yi+ [ Select) 2 + 4y ( Select) Y1-Select ] |Select 1 +y2+ [Select] S 10 y+( Select ) 2+ ( Select ) 20 2 20 ys 20 Question 4

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