Maximize $z = 4x_1+ 3x_2 + 6x_3$

Subject to $2x_1 + 3x_2 + 2x_3 ≤ 440 \\ 4x_1 + 3x_3 ≤ 470 \\ 2x_1 + 5x_2 ≤ 430\\ X_1, x_2, x_3 ≤ 0$

Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 06

Year : MAY 2015

Standard form:

Maximize $z=4x_1+3x_2+6x_3+0s_1+0s_2+0s_3;$

Constraint:

$2x_1+3x_2+2x_3+1s_1+0s_2+0s_3=440 ; \\ 4x_1+0x_2+3x_3+0s_1+1s_2+0s_3=470 \\ 2x_1+5x_2+0x_3+0s_1+0s_2+1s_3=430 \\ x_1,x_2,x_3,s_1,s_2,s_3 \geq 0$

For maximization: $x_1=0; x_2=(380/9)=42.22; x_3=(470/3)=156.67 \\ Z_{max}=3200/3=1066.67$