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The optimal value x 1 and x 2 for the maximize output. The optimal value x 1 and x 2 for the maximize output is ( 300 , 200 ) _ . In the problem given that total output of large step ladders by producing x 1 of them by a process P 1 and x 2 by a process. It means that f = x 1 + x 2 . If f is the total profit. From the given data the inequalities are written as: 2 x 1 + 3 x 2 ≤ 1200 4 x 1 +2 x 2 ≤ 1600 Convert all the inequalities equation in the form of x 2 = m x 1 + c . Where c is constant and m is the line slope. The equation 2 x 1 + 3 x 2 ≤ 1200 which follows as: 2 x 1 + 3 x 2 = 1200 3 x 2 = 1200 − 2 x 1 x 2 = 400 − 0.67 x 1 Same as the inequality’s equation 4 x 1 +2 x 2 ≤ 1600 follow as line x 2 = 800 − 2 x 1 . The common region of the given inequalities is below lines x 2 = 400 − 0.67 x 1 and x 2 = 800 − 2 x 1 respectively. Figure 1 say that the shaded common area is between points ( 0 , 0 ) , ( 400 , 0 ) , ( 300 , 200 ) and ( 0 , 400 ) . max ( f ) ( 400 , 0 ) = 400 + 0 = 400 Same as the value of max ( f ) ( 300 , 200 ) and max ( f ) ( 0 , 400 ) are 500 and 400 respectively. From the above calculation of objective function at different points, say that max ( f ) = 500 is largest value from the others. Therefore, the optimal value x 1 and x 2 for the maximize output is ( 300 , 200 ) _ .

The optimal value x 1 and x 2 for the maximize output. The optimal value x 1 and x 2 for the maximize output is ( 300 , 200 ) _ . In the problem given that total output of large step ladders by producing x 1 of them by a process P 1 and x 2 by a process. It means that f = x 1 + x 2 . If f is the total profit. From the given data the inequalities are written as: 2 x 1 + 3 x 2 ≤ 1200 4 x 1 +2 x 2 ≤ 1600 Convert all the inequalities equation in the form of x 2 = m x 1 + c . Where c is constant and m is the line slope. The equation 2 x 1 + 3 x 2 ≤ 1200 which follows as: 2 x 1 + 3 x 2 = 1200 3 x 2 = 1200 − 2 x 1 x 2 = 400 − 0.67 x 1 Same as the inequality’s equation 4 x 1 +2 x 2 ≤ 1600 follow as line x 2 = 800 − 2 x 1 . The common region of the given inequalities is below lines x 2 = 400 − 0.67 x 1 and x 2 = 800 − 2 x 1 respectively. Figure 1 say that the shaded common area is between points ( 0 , 0 ) , ( 400 , 0 ) , ( 300 , 200 ) and ( 0 , 400 ) . max ( f ) ( 400 , 0 ) = 400 + 0 = 400 Same as the value of max ( f ) ( 300 , 200 ) and max ( f ) ( 0 , 400 ) are 500 and 400 respectively. From the above calculation of objective function at different points, say that max ( f ) = 500 is largest value from the others. Therefore, the optimal value x 1 and x 2 for the maximize output is ( 300 , 200 ) _ .

Advanced Engineering Mathematics

Advanced Engineering Mathematics

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Chapter 22 Solutions

Advanced Engineering Mathematics

Ch. 22.1 - Prob. 1P Ch. 22.1 - Prob. 2P Ch. 22.1 - Prob. 3P Ch. 22.1 - Prob. 4P Ch. 22.1 - Prob. 5P Ch. 22.1 - Prob. 6P Ch. 22.1 - Prob. 7P Ch. 22.1 - Prob. 8P Ch. 22.1 - Prob. 9P Ch. 22.1 - CAS EXPERIMENT. Steepest Descent. (a) Write a...

Ch. 22.2 - Prob. 1P Ch. 22.2 - Prob. 2P Ch. 22.2 - Prob. 3P Ch. 22.2 - Prob. 4P Ch. 22.2 - Prob. 5P Ch. 22.2 - Prob. 6P Ch. 22.2 - Prob. 8P Ch. 22.2 - Prob. 9P Ch. 22.2 - Prob. 10P Ch. 22.2 - Prob. 11P Ch. 22.2 - Prob. 12P Ch. 22.2 - Prob. 13P Ch. 22.2 - Prob. 14P Ch. 22.2 - Prob. 15P Ch. 22.2 - Prob. 16P Ch. 22.2 - Prob. 17P Ch. 22.2 - Prob. 18P Ch. 22.2 - Prob. 19P Ch. 22.2 - Prob. 20P Ch. 22.2 - Prob. 21P Ch. 22.2 - Prob. 22P Ch. 22.3 - Prob. 1P Ch. 22.3 - Prob. 2P Ch. 22.3 - Prob. 3P Ch. 22.3 - Prob. 4P Ch. 22.3 - Prob. 5P Ch. 22.3 - Prob. 6P Ch. 22.3 - Prob. 7P Ch. 22.3 - Prob. 8P Ch. 22.3 - Prob. 9P Ch. 22.3 - Prob. 10P Ch. 22.3 - Prob. 11P Ch. 22.3 - Prob. 12P Ch. 22.3 - Prob. 13P Ch. 22.3 - Prob. 14P Ch. 22.4 - Prob. 1P Ch. 22.4 - Prob. 2P Ch. 22.4 - Prob. 3P Ch. 22.4 - Prob. 4P Ch. 22.4 - Prob. 6P Ch. 22.4 - Prob. 7P Ch. 22.4 - Prob. 8P Ch. 22.4 - Prob. 9P Ch. 22 - Prob. 1RQ Ch. 22 - Prob. 2RQ Ch. 22 - Prob. 3RQ Ch. 22 - Prob. 4RQ Ch. 22 - Prob. 5RQ Ch. 22 - Prob. 7RQ Ch. 22 - Prob. 8RQ Ch. 22 - Prob. 9RQ Ch. 22 - Prob. 10RQ Ch. 22 - Prob. 11RQ Ch. 22 - Prob. 13RQ Ch. 22 - Prob. 14RQ Ch. 22 - Prob. 15RQ Ch. 22 - Prob. 16RQ Ch. 22 - Prob. 17RQ Ch. 22 - Prob. 18RQ Ch. 22 - Prob. 19RQ Ch. 22 - Prob. 20RQ

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