Question

Yakune Coffee Shop at the Galleria Mall serves two coffee blends it brews on a daily basis, Costa Rica and Yakune Blend. Each is a blend of three high-quality coffees from Colombia, Kenya, and Indonesia. The coffee shop has 10 pounds of each of these coffees available each day. Each pound of coffee will produce sixteen 16-oz cups of coffee. The shop has enough brewing capacity to brew 38 gallons of these two coffee blends each day. The shop sells 1.5 times more Costa Rica than Yakune Blend each day. Costa Rica sells for $2.20 per cup, and Yakune Blend sells for $1.55 per cup. Costa Rica is a blend of 15% Colombian, 25% Kenyan, and 60% Indonesian, while Yakune is a blend of 65% Colombian, 15% Kenyan, and 20% Indonesian.

The manager wants to know how many cups of each blend to sell each day in order to maximize revenue. Formulate a linear programming model for this problem. [Note: 1 gallon = 128 oz; 1 oz = 0.0625 pounds]

Answer 1

1 cup = 16-oz = 1 lb
1 gallon = 128 oz = 8 lb
So,
38 gallons = 304 lbs.

Let 'C' and 'Y' be the cups (or pounds) of Costa Rica and Yakune Blend to be produced.

Max Z = 2.20 C + 1.55 Y

Subject to,

0.15 C + 0.65 Y <= 10 (Colombian coffee)

0.25 C + 0.15 Y <= 10 (Kenyan coffee)

0.60 C + 0.20 Y <= 10 (Indonesian coffee)

C >= 1.5 Y (ratio of C and Y)

C + B <= 304 (brewing capacity)

C, Y >= 0