$i,$ and $d_{ni}$ be the deviation variable which is less than the value of $i,$ for $i=1,2.)$

Min

s$.$t$.$

Material $1$

Material $2^{|}$

Material $3$

Goal $1$

Goal $2$

$x_i,d_{ni},d_{}0,$ for $i=1,2$

$($c$)$ Use the graphical goal programming procedure to find the optimal solution for the model formulated in part $($b$).$

$(x_1,x_2)=()$

$($d$)$ If goal $1$ is twice as important as goal $2,$ what is the optimal product mix?

$(x_1,x_2)=()$