The Star City Caf at a U.S. campus student centre serves two coffee blends it brews daily,

The Star City Café at a U.S. campus student centre serves two coffee blends it brews daily, Morning Blend and Study Break. Each is a blend of three high-quality coffees from Brazil, Tanzania, and Guatemala. The Cafe has 5 lbs. of each of these coffees available each day. Each pound of coffee will produce sixteen 16-oz cups of coffee, and the Cafe has enough brewing capacity to brew 25 gallons of the two coffee blends each day. Morning Blend includes 25% Brazilian, 30% Tanzanian, and 45% Guatemalan, while Study Break is a blend of 55% Brazilian, 15% Tanzanian, and 30% Guatemalan. The shop sells one and a half times more Morning Blend than Study Break each day. Morning Blend sells for $1.95 per cup, and Study Break sells for $1.70 per cup. The manager wants to know the number of cups of each blend to sell each day to maximize sales.
a. Formulate a linear programming model for this problem.
b. Solve this model using graphical analysis.
c. Solve this model using Excel.
d. If the Café could get one more pound of coffee, which one should it be? What would be the effect on sales of getting one more pound of this coffee?
e. Would it benefit the shop to increase its brewing capacity from 25 gallons to 30 gallons?
f. Should the Cafe spend $25 per day on advertising if it would increase the relative demand for Morning Blend to twice that of Study Break?