Gillian's Restaurant has an ice cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons of both products. A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs $0.93, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15, and the profit per gallon of yogurt is $3.60.
a) Formulate a linear programming model for this problem. Be sure to include all constraints.
b) Solve this problem using graphical techniques.
Do not submit the graph. In your answer, include each of the corner points and the Z value associated with each of the corner points. Highlight the corner point that optimizes the solution. If there is no feasible solution, then indicate so. If the solution lies along a constraint equation, then indicate the constraint equation and the bounds for x1 and x2.