Solve the following linear programming problem:

Maximize: $12$ x$1+21$ x$2+7$ x$3+15$ x$4$

Subject to:

$4$ x$1+3$ x$2+2$ x$3+5$ x$4...400$

$2$ x$1+1\mathrm{.}5$ x$2+3\mathrm{.}3$ x$3+2$ x$4...150$

x$145$

x$2...100$

x$1,$ x$2,$ x$3,$ x$40($nonnegative$)$

Rework the linear programming application example presented in this chapter

with a new objective function. This time, the objective will be to minimize a $$distaste

factor$$ rather than cost. The distaste factor can have a value between $1$ and $10,$

where

$1$I don$$t mind this food at all; serve it up$!$

$4$I can eat some of it$,$ but tire of it quickly.

$8$I would prefer not to eat this food.

$10$I$$ll gag if I have to eat this food.

The distaste factors are obviously specific to each individual, but a set of distaste fac$-$

tors has been assigned to each food in the following table: