1. Gillian's Restaurant in Vaudreuil has an ice cream counter where two main products are sold in a variety of flavours: ice cream and frozen yogurt. The restaurant places an order with its ice cream and yogurt suppliers every week. The store has enough freezer space to store 115 gallons of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs S$0.93. The restaurant plans a budget of S90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. The profit per gallon of ice cream is $4.15 and the profit per gallon of yogurt is $3.60. 1. Algebraically formulate a linear programming model to represent this problem. Define the decision variables, objective function, and constraints. Use the graphical method to solve this model. 3. Present the optimal solution to this problem using a business statement. (Complete sentence to present the solution to your supervisor). 4. What additional profit would the restaurant realize each week if the freezer capacity could accommodate an additional 20 total gallons of ice cream and yogurt? Justify your answer (hint: graphically). 2. Consider the following four linear programming model formulations. Using the graphical method, determine: 1. the formulation that has more than one optimal solution . the formulation that is unbounded 3. the formulation that has no admissible solution 4. the formulation that has a single optimal solution Formulation 1 Max: 10X + 10Y Tel que : 2X + 4Y <= 16 4Y <= 8 X >= 6 X,Y >= 0. Formulation 2 Max: Tel que : X+2Y X X +2Y <= 2 2Y <=2 X Y>=0 Formulation 3 Max: Tel que: 3X + 2Y X>=2 + Y>=5 2Y>=8 X,Y>=0 Formulation 4 Min: Tel que: 3X + 3Y 4X + 6Y <= 48 4X +2Y<=12 3Y>= 3 2X>=2 X,Y = 0