Optimization methods. SOLVE BY SENSITIVITY-ADD VARIABLE

Exercise 2.- A factory can produce four products denoted by P1, P2, P3 and P4. Each product must be processed in each of two workshops. The processing times in hours per unit produced) are given in the following table. 400 hours of labour are available in each workshop. The profit margins are 4, 6, 10, and 9 dollars per unit of P1, P2, P3 and P4 produced, respectively. Everything that is produced can be sold. w1 3 8 5 6 8 W2 6 2 X2 X4 51 S2 X1 3 6 X3 8 RHS 400 4 6 1 S1 S2 0 Ratio SO 80 5 8 0 1 400 2 6 Z 4 10 9 0 0 X3 S2 0 1 X3 S2 X2 1/2 1/2 1/1 X4 3/4 17/4 RHS 50 150 -500 Ratio 200/3 600/17 0 1 Z 0 3/2 0 3/8 33/8 1/4 X1 6/17 33/34 X2 X3 X4 RHS 0 S1 1/8 5/8 . 5/4 51 4/17 5/34 35/34 si 2/5 - 1/10 1 0 X3 X4 Z 10/17 - 2/17 20/17 Ratio 40 -300 0 1 0 0 S2 3/17 4/17 6/17 S2 3/10 1/5 400/17 600/17 -9400/17 RHS 40 40 X2 41/34 xi - 3/5 9/10 - 1/2 X4 Ratio 1 X3 17/10 1/5 0 X4 0 1 Z 0 0 -600 a) New Product W1 5 W2 5 Sales Price 5 XS Conclusion a) New Product W1 5 W2 7 Sales Price 9 X5 X1 X2 X3 X4 X5 $1 S2 RHS Ratio The tableau is not longer Sole with Solve with Entering Variable Leaving Variable Exercise 2.- A factory can produce four products denoted by P1, P2, P3 and P4. Each product must be processed in each of two workshops. The processing times in hours per unit produced) are given in the following table. 400 hours of labour are available in each workshop. The profit margins are 4, 6, 10, and 9 dollars per unit of P1, P2, P3 and P4 produced, respectively. Everything that is produced can be sold. w1 3 8 5 6 8 W2 6 2 X2 X4 51 S2 X1 3 6 X3 8 RHS 400 4 6 1 S1 S2 0 Ratio SO 80 5 8 0 1 400 2 6 Z 4 10 9 0 0 X3 S2 0 1 X3 S2 X2 1/2 1/2 1/1 X4 3/4 17/4 RHS 50 150 -500 Ratio 200/3 600/17 0 1 Z 0 3/2 0 3/8 33/8 1/4 X1 6/17 33/34 X2 X3 X4 RHS 0 S1 1/8 5/8 . 5/4 51 4/17 5/34 35/34 si 2/5 - 1/10 1 0 X3 X4 Z 10/17 - 2/17 20/17 Ratio 40 -300 0 1 0 0 S2 3/17 4/17 6/17 S2 3/10 1/5 400/17 600/17 -9400/17 RHS 40 40 X2 41/34 xi - 3/5 9/10 - 1/2 X4 Ratio 1 X3 17/10 1/5 0 X4 0 1 Z 0 0 -600 a) New Product W1 5 W2 5 Sales Price 5 XS Conclusion a) New Product W1 5 W2 7 Sales Price 9 X5 X1 X2 X3 X4 X5 $1 S2 RHS Ratio The tableau is not longer Sole with Solve with Entering Variable Leaving Variable