3x+7y+12z=6x+6y+6z
z=x/2-y/6
x+y+z=(3/2)x+(5/6)y
0<=x<=200
0<=y<=200
0<=x/2-y/6<=200
3x-1200<=y<=3x
でプログラムを組んで

f=\(x,y){
if(x<0|x>200|y<0|y>200|y<3*x-1200|y>3*x) return(0)
else return((3/2)*x+(5/6)*y)
}

> optim(c(100,100),\(xy) f(xy[1],xy[2]),control = list(fnscale=-1))
$par
[1] 200 200

$value
[1] 466.6667

$counts
function gradient
223 NA

$convergence
[1] 0

$message
NULL
x=200
y=200
のとき最大値466.6667

検算終了！