Formulate algebraically the linear programming model

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Reference no: EM132465212

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:

special : at least 40% columbian, at least 30% mocha
dark : at least 60% Brazilian, no more than 10% mild
regular : no more than 60% mild, at least 60% Brazilian

selling price per pound of each blend

special = $6.50
dark = $5.25
regular = $3.75

The cost of Brazilian coffee is $2.00 per 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 the NET profit.

a. Formulate algebraically the Linear Programming (LP) model for this problem.

b. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel Solver (Provide the corresponding "Excel Spreadsheet" and the "Sensitivity Report"). Include "managerial statements" that communicate the results of the analyses.

c. Are there multiple optimal solutions? Justify

Reference no: EM132465212

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