Calculating the amount of coffee prepared to maximize profit

Question

Problem:

1. The Mill Mountain Coffee Shop blends coffee on the premises for its customers. It sells three basic blends in 1-pound bags, Special Mountain Dark, and Mill Regular. It uses four different types of coffee to produce the blends - Brazilian, mocha, Columbian, and mild. The shop used the following blend recipe requirements.

Blend                               Mix Requirements                          Selling Price/lb($)

Special          At least 40% Columbian, at least 30% mocha               6.50

Dark             At least 60% Brazilian, no more than 10% mild            5.25

Regular        No more than 60% mild, at least 30% Brazilian            3.75                           

The cost of Brazilian coffee is $2.00 per, the pound, the cost of mocha is $2.75 per pound, the cost of Columbian is $2.90 per pound, and the cost of mild is $1.70 per pound. The shop has 110 pounds of Brazilian coffee, 70 pounds of mocha, 80 pounds of Columbian, and 150 pounds of mild coffee available per week. The shop wants to know the amount of each blend it should prepare each week to maximize profit.

1. Formulate a Linear programming model for this problem.
2. Solve this model using the computer.