Problem #$1$ Lorie Nutritional Diet Planning $($This problem includes $14$ questions Questions $1$ to $14)$Lorie$,$ a diet nutritionist, is working to create a diet plan for a healthy human consumption. She believes that a healthy diet should be made to consist of three possible foods, namely apples, bread and corn. She is planning the diet to provide calories, vitamin X and mineral Y$.$ Lorie gathers the information for the diet problem and summarized it in the table seen below.All of questions $1$ to $15$ referred to Lorie Diet Problem. Use the sensitivity analysis results seen in Table A seen above to perform the necessary calculations to answer the following $15$ questions in the multiple$-$choice space of the final exam.Question #$1$: the optimal total minimum cost of Lorie nutritional plan is:Question #$2$: Which of the nutritional constraints are fully utilized $($or requirements are exactly met$)?$Question #$3$: The daily cost of food for a group of $1,000-$personinstitution $($in dollars$)$ is:$$Questions #$4$: How many calories will Lorie be recommending to supply daily to each person in the nutritional program?Question #$5$: Which food is not recommended for inclusion in the program?$$Question #$6$: If a certain food is not in the optimal diet, what should the price of this food be to make it attractive enough to be included in the solution $($in cents, approximately$)?$Question #$7$: What is the utilization level of bread $($in percentage, approximately$)?$Question #$8$: Suppose we increase the requirement of Vitamin X from $150$ to $155$; the cost of the diet, in such a case, will be $($in cents, per person, per day, approximately$)$ what amount?$$Question #$9$: What is the necessary condition $($or conditions$)$ which can motivate Lorie to require the inclusion of more apples in the nutritional program in a cost$-$effective way?$$Question #$10$: Why is dual price of the Apples requirement $($i$.$e$.,$ constraint $6)$ equal to zero?$$Question #$11$: In the right$-$hand side $($RHS$)$ sensitivity analysis $($in constraint #$2),$there is no upper limit$.$ This is because: $$Question #$12$: How much money can be saved, per person, per day, in cents, if the mineral requirement is changed from $60$ t$055($approximately$)?$Question #$13$: Assume that the price of apples increases $10$ percent; the diet composition in such a case will:Question #$14$: Is it possible that the optimal solution will include corn only, if the price of corn is low enough?