Comparatively this may take longer to answer than other questions, but this also has a substantially more weight$)$

We need to create a diet that minimizes cost while meeting the nutritional requirements. A simplified set of data using five food items and three nutritional ingredients is given below:

Cost of food items:

food

$$/$pound

milk

$0\mathrm{.}80$

egg

$1\mathrm{.}20$

bread

$1\mathrm{.}40$

cheese

$6\mathrm{.}00$

oats

$1\mathrm{.}20$

Nutritional content:

food

grams of carbohydrates per pound

grams of protein per pound

grams of fat per pound

milk

$20$

$15$

$15$

egg

$4$

$60$

$45$

bread

$225$

$45$

$20$

cheese

$8$

$104$

$130$

oats

$450$

$50$

$25$

Daily requirements:

grams of carbohydrates

grams of protein

grams of fat

minimum

$250$

$40$

$60$

maximum

$350$

$70$

$80$

We need to find the minimum cost diet for a day. $($Ignore any taste or other considerations!$)$

For your answer, please include the following:

$1.$ What framework or methodology is appropriate for solving this problem? $($such as simulation, optimization, decision theory, etc.$)$

$2.$ How can this problem be formulated using the above framework?

$3.$ What technology $($software$,$ tool$)$ is appropriate for solving this problem?

$4.$ Using the appropriate technology, what is the solution to this problem? $($Provide the pounds of each food item to be included in the diet, as well as the cost of the diet. Fractional values are permissible $-$ please provide two decimal places.$)$