Question #$2$: Restaurant B has an ice$-$cream counter where it sells two main products, ice$-$cream and frozen yogurt, each in 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 total of both products. A gallon of frozen yogurt costs $$0\mathrm{.}75$ and a gallon of icecream costs $$0\mathrm{.}93,$ and the restaurant budgets $$90$ per week for these products. The manager estimates that each week the restaurant sells at least twice as much ice$-$cream as frozen yogurt. Profit per gallon of ice cream is $$4\mathrm{.}15,$ and profit per gallon of yogurt is $$3\mathrm{.}60.$

a$.$ Formulate a linear prgramming model for this problem.

b$.$ Solve this problem by using graphical analysis.

c$.$ Solve with Excel as well.

d$.$ How much additional profit would the restaurant realize each week if it increased its freezer capacity to accomodate $20$ extra gallons total of ice cream and yogurt?

e$.$ Perform sensitivity analysis on Excel and compare your answer for part d with Excel solution!