Question 2

Linear Programming

The Star City Cafe 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 (which translates to 80 cups of coffee). And the Cafe has enough brewing capacity to brew 25 gallons of the two coffee blends each day, that translates to 200 cups. 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 twice as more Morning Blend than Study Break each day. Morning Blend sells for $2.00 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 profits.

1. Formulate a linear programming model in Excel and solve it. Keep your solution to the whole number of cups.
2. Would it benefit the shop to increase its brewing capacity from 25 gallons to 30 gallons (from 200 cups to 240 cups)?
3. Should the Cafe spend $25 per day on advertising if it would increase the relative demand for Morning Blend to three times that of Study Break?