There are two food items (Food I and Food II) that can be combined to design a diet with certain characteristics. The nutrient content of the two items as well as the minimum nutrient requirements for the diet are as shown below. The is also a maximum limit put on one of the nutrients (Energy). The prices of the two food items are 2.0 and 3.0 per unit. a) Write out the mathematical formulation of the problem (objective function and constraints). b) Draw the boundary conditions for the problem and identify the feasible region by shading. c) Solve for the optimal solution and state what combinations of the two foods would constitute the optimal diet and what the diet would cost. Mark the optimal solution on the diagram. d) How would the optimal solution change if the price of Food I halves? There are two food items (Food I and Food II) that can be combined to design a diet with certain characteristics. The nutrient content of the two items as well as the minimum nutrient requirements for the diet are as shown below. The is also a maximum limit put on one of the nutrients (Energy). The prices of the two food items are 2.0 and 3.0 per unit. a) Write out the mathematical formulation of the problem (objective function and constraints). b) Draw the boundary conditions for the problem and identify the feasible region by shading. c) Solve for the optimal solution and state what combinations of the two foods would constitute the optimal diet and what the diet would cost. Mark the optimal solution on the diagram. d) How would the optimal solution change if the price of Food I halves