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MATHS - STATS PROBLEMS WITH SOLUTIONS

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Question;1 write the initial tableau for the following linear programing problem.do not solvez=10x + 6x -8x5x-2x+6x R1-5R2 + R3 - - > R3X x x s s z1 3 3 1 0 0 500 2 10 2 1 0 1400 -3 -14 8 0 1 400BX x x s s s z2 2 1 1 0 0 0 121 2 3 0 1 0 0 453 -1 1 0 0 1 0 -2-2 -1 1 0 0 1 0 0CX x x s s a z15 11 7 1 0 0 0 305 8 1 0 1 0 0 72-2 6 3 0 0 1 0 30-55 -75 2 0 0 0 1 45010- given the following linear programing problem and final tableau state the optimal solutionMaximize z = 1.75x + 5x subject toX + 5x = 8X,x,x>= 012- given the following final tableau that was solved using the dual method state the optimal where it occursY y x x x w0 1 ? -1 0 0 81 0 -1/2 2 0 0 40 0 2 -9 1 0 120 0 5 10 0 1 32013- given the following linear programing problem write the initial tableauAMaximize z= 3x + 2x subject toX + 3x =4X,x >= 0BMinimize z=15x ? 10x subject to5x + 3x = 4X,x>=014- given the following final tableau for a minimization problem that was solved by maximizing the opposite of the objective,state the minimal value and where it occursX x x s s s w2 0 1 2 0 -1 0 4010 0 0 -40 1 10 0 8000 1 0 -1 0 1 0 60100 0 0 100 0 100 1 -2600015- given the following linear programing problem,write the initial tableauMaximize z=3x + 4 x subject to5x + 2x =016- this tableau is a final tableau,write the solution assuming the original problem was a standard maximization problem. pivot one time using row 2 column 2 and then compare the tableau to the one given and interpret the results.X x s s s z0 23/3 1 0 -2/3 0 940 5/3 0 1 -2/3 0 101 2/3 0 0 1/3 0 250 0 0 0 5 1 37517- graph the feasible region for the following system of inequalities-2 < x =60<=y<=20<=x<=420- to pour a concrete sidewalk takes 2 hrs of preparation and 3hrs of finishing. To pour a concrete patio takes 4 hrs of preparation and 3 hrs of finishing. There are 8 hrs available for preparation and 21 hrs available for finishing. ABC concrete company makes a profit of $450on a sidewalk and $700 on a patio how many sidewalks and patios should the company construct to maximize the profit? Setup a system of inequalities for this problem, identify all variables used, and give the objective function but don?t solve.ObjectiveConstraints

 

Paper#61030 | Written in 18-Jul-2015

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