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:

Food # $12345678910$

Name Rice Cabbage Spinach Peanuts Or$.$ Juice Tuna Turkey Pork Bread

Lima

Beans

Nutrient

Thiamin mg $0000\mathrm{.}40\mathrm{.}2000\mathrm{.}800\mathrm{.}4$

Riboflavin mg $000\mathrm{.}1000\mathrm{.}1000\mathrm{.}80$

Niacin mg $4002001010600$

Folic Acid mg $112312320109000078$

Vitamin C mg $01242806400009$

Distaste Factor $1431121317$

Cost $ $0\mathrm{.}250\mathrm{.}170\mathrm{.}350\mathrm{.}950\mathrm{.}751\mathrm{.}450\mathrm{.}851\mathrm{.}850\mathrm{.}150\mathrm{.}35$

$414$ Chapter $9$ Iterative Solutions Using Excel

a$.$ Solve the linear programming problem to minimize distaste factor while

still satisfying each of the nutritional constraints listed in the application

example. How many servings of each type of food are needed, and what

is the overall distaste level?

b$.$ Create your own set of distaste factors for these foods and repeat step $($a$).$