A dietician has decided to go on a steady diet of only two foods for all his meals: Potatos and Steak. He realizes that this isn't the healthiest diet, so he wants to make sure that he eats the right quantities of the two foods to satisfy some key nutritional requirements. He has obtained the following nutritional and cost information:

Grams of Ingredient per serving
Ingredient Steak Potatoes Daily Requirement
(Grams)
Carbohydrates 5 15 At least 50
Protein 20 5 At least 40
Fat 15 2 At most 60
Cost per serving $5 $2

Ralph wishes to determine the number of daily servings (may be fractional) of steak and potatoes that will the dietician this requirements at a minimum cost.
a. Formulate a linear programming model for this problem.
b. Use the graphical method to solve this model. Give the optimal solution and the optimal cost.