$2.$Part a$)$: A student wants to create the perfect daily meal plan consisting of two foods, fried chicken and instant ramen. Each serving of fried chicken contains $8$ grams of protein, $12$ grams of fat, and $4$ grams of carbohydrates. Each serving of instant ramen contains $4$ grams of protein, $8$ grams of fat, and $8$ grams of carbohydrates. The student wants to have at least $40$ grams of protein, $48$ grams

of fat, and $48$ grams of carbohydrates in the meal plan. Fried chicken costs $$4$ per serving and food ramen costs $$3$ per serving. Formulate the problem as a linear programming problem to minimize the cost while meeting the nutritional requirements. Give a $($very$)$ short description of what each constraint means. Sketch the feasible region, find the optimal solution or a certificate of unboundedness and sketch the line of points which give objective

value equal to the maximum objective value you found, if the problem was not unbounded. be sure to check unbounded

Part b$)$: Rewrite the LP that you got in part a$)$ in LP standard form.