The North York Health is a weight management centre, producing a wide variety of frozen microwavable dinners for consumption by its clients. The microwavable dinners are strictly monitored for nutritional content to ensure that clients eat a balanced diet. One new microwavable dinner will be the "North York beef sirloin tips dinner," with product code NY-11. It will consist of beef tips and gravy, plus some combination of peas, carrots, and a dinner roll. North York Health would like to determine what quantity of each item to include in NY-11 in order to meet nutritional requirements, while costing as little as possible. The nutritional and cost information for each item in NY-11 are given in the following table:

Calories Vitamin A Vitamin C Protein
Calories from Fat IUs milligrams grams Cost
Item (per oz.) (per oz.) (per oz.) (per oz.) (per oz.) (per oz.)
Beef Tips 54 19 0 0 8 $0.40
Gravy 20 15 0 1 0 $0.375
Peas 15 0 15 3 1 $0.25
Carrots 8 0 90 1 1 $0.20
Dinner Roll 40 10 0 0 1 $0.38

The nutritional requirements for NY-11 are as follows: (1) it must have between 300 and 350 calories, (2) calories from fat should be no more than 30% of the total number of calories, and (3) it must have at least 500 IUs of vitamin A, 15 milligrams of vitamin C, and 30 grams of protein. Moreover, for practical reasons, NY-11 must include at least three ounces of beef but no more than five ounces of carrots. It must have at least half an ounce of gravy for every ounce of beef.

Required:

(a) Define decision variables clearly.
(b) Formulate this as a linear programming problem and solve it with a detailed description of your output. Please include all output information.
(c) Specify the reported optimal solution and optimal objective function value in the language of the problem (in English and without using variable symbols).
(d) Which of the technical constraints will involve slack variables if the LP is converted to standard form?
(e) Which of the technical constraints are binding at the reported optimal solution?
(f) If the cost per ounce of peas goes down by five cents, will the reported optimal solution still be optimal? Briefly explain/support your answer citing relevant figures, if any, from the output.
(g) If NY-11 should contain at least 515 IUs of vitamin A, by how much the current optimal objective function value will increase or decrease? Briefly explain/support your answer citing relevant figures, if any, from the output.
(h) What should change - and by how much - in order for the NY-11 to possibly include at least some dinner roll?