$***$SOLVE PART B PLEASE$***$

Suppose that there are three types of food available for Joe: corn, bread and $2\%$ milk.

Considering Joe's nutritional needs, the number of calories he needs to take has to be between

$2000$ and $2250$ cal. and the amount of Vitamin A he needs to take has to be between $5000$ and

$50000g.$ The table below lists, the cost per serving, the amount of Vitamin A per serving, and

the number of calories per serving for each type of food.

Assuming that maximum serving size for each type of food is $10$ :

a$)[5$pt$]$ Formulate a linear programming problem mathematically to find the optimal diet

as a mix of three types of food that minimizes the cost. Clearly define the decision

variables, objective and constraints.

b$)[5$pt$]$ Solve the linear programming problem defined in part a$)$ using Excel's solver or

Python's linprog function. Report the values of the decision variables, the objective

function at the optimal solution. $($You will get fractional numbers at the optimal solution.

Do not round them$)$