A coffee shop blends coffee on the premises for its customers. It sells the following three basic blends: Special, Dark and Regular. To produce the blends, the shop must use three different types of coffee: Brazilian, mocha, and Colombian. The shop has the following bland recipe requirements:
Special blend: No more than 60% Brazilian coffee should be included. Dark blend: At least 40% Colombian coffee should be included. Regular blend: No more than 30% mocha coffee should be included. The shop has at least 140 pounds of Colombian coffee per week. The shop sells the special blend for $6.50 per pound, the dark blend for $5.90 per pound, and the regular blend for $4.10 per pound. Moreover, the cost of Brazilian coffee is $2.00 per pound, the cost of mocha is $2.75 per pound, and the cost of Colombian is $2.90 per pound. The shop wants to know the amount of each blend it should prepare each week to maximize profit. [Note: Xij= lbs. of coffee i used in blend j per week, where i = 1 (Brazilian), 2 (Mocha), 3 (Colombian), and products j = s (special), d (dark), r (regular)
The objective function for the model is Max Z = 6.50(X1s + X2s + X3s + X4s) + 5.90(X1d + X2d + X3d + X4d) + 4.10(X1r + X2r + X3r + X4r) -2.0(X1s + X1d + X1r) - 2.75(X2s + X2d + X2r) - 2.9(X3s + X3d + X3r) - 1.7(X4s + X4d + X4r). O True O False