Max $z = 15x_1 + 6x_2+ 9x_3 + 2x_4\\ \space s.t. \space 2x_1 + x_2 + 5x_3 + 6x_4 ≤ 20 \\ 3x_1 + x_2 + 3x_3 + 25x_4 ≤ 24 \\ 7x_1 + x_4 ≤ 70 \\ \&\space \space x_1, x_2, x_3 , x_4 ≥ 0 $

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 06

Year : MAY 2014

In standard form,

Maximize, $z=15x_1+6x_2+9x_3+2x_4+0s_1+0s_2+0s_3;$

Constraints:

$2x_1+1x_2+5x_3+6x_4+1s_1+0s_2+0s_3=20; \\ 3x_1+1x_2+3x_3+25x_4+0s_1+1s_2+0s_3=24; \\ 7x_1+0x_2+0x_3+1x_4+0s_1+0s_2+1s_3=70; \\ x_1+x_2+x_3+x_4+s_1+s_2+s_3 ≥ 0$

For Maximization; $X_1=4; X_2=12; X_3==0; X_4=0; Z_{max}=132.$