question archive The Mill Mountain Coffee Shop blends coffee on the premises for its customers
The Mill Mountain Coffee Shop blends coffee on the premises for its customers
Subject:StatisticsPrice: Bought3
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, Colombian, and mild. The shop has the following blend recipe requirements:
Blend Mix requirements Selling price ($)/pound
Special: At least 40% Columbian, at least 30% mocha 6.5
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 pound, the cost of mocha is $2.75 per pound, the cost of Colombian 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 Colombian, 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.
Please use integer programming to solve the following:
A) Formulate a linear programming model for this problem using excel.
B). Solve the problem by using the computer. What are the optimal values for each decision variable? What is the optimal value for the objective function?
C) Which coffees (Brazilian, Mocha, Columbian, and Mild) have slack (non-binding) constraints? What are the shadow prices for these constraints?
D) Which coffees (Brazilian, Mocha, Columbian, and Mild) have binding constraints? Calculate the shadow price for Brazilian using an increment of 10 pounds.
