Wildcat Coffee Inc., uses four types of coffee beans (Columbia, Java, Brazil, an

Question

Wildcat Coffee Inc., uses four types of coffee beans (Columbia, Java, Brazil, and South Africa) as mixtures to manufacture its three coffee products (Everyday, Energy, and Excellence). The cost per pound, the availability, and rating information of the coffee beans are as follows.

Coffee product tests are used to provide ratings on a scale of 0-100, with higher ratings indicating higher product performance. Here are the three coffee products and their product information:

Due to the popular demand of the gourmet segment, at least 920 pounds of Excellence must be produced.

Set up a linear programming model for the above problem.

Coffe Bean Cost Per Pound Caffeine Rating Taste Ratting Aroma Rating Availabie Pounds Columbia 2.10 68 89 90 700 Java 1.50 79 65 77 850 Brazil 1.75 81 78 95 1000 South Africa 1.15 58 68 59 1200

Explanation / Answer

Decision variable:

DC = pounds of Columbia beans used to produce Everyday coffee

DJ = pounds of Java beans used to produce Everyday coffee

DB = pounds of Brazil beans used to produce Everyday coffee

DS = pounds of South Africa beans used to produce Everyday coffee

NC = pounds of Columbia beans used to produce Energy coffee

NJ = pounds of Java beans used to produce Energy coffee

NB = pounds of Brazil beans used to produce Energy coffee

NS = pounds of South Africa beans used to produce Energy coffee

XC = pounds of Columbia beans used to produce Excellence coffee

XJ = pounds of Java beans used to produce Excellence coffee

XB = pounds of Brazil beans used to produce Excellence coffee

XS = pounds of South Africa beans used to produce Excellence coffee

Objective: Max 2.2*(DC+DJ+DB+DS)+2.8*(NC+NJ+NB+NS)+3.5*(XC+XJ+XB+XS) - 2.1*(DC+NC+XC) - 1.5*(DJ+NJ+XJ) - 1.75*(DB+NB+XB) - 1.15*(DS+NS+XS)

s.t. Constraints:

DC+NC+XC <= 700

DJ+NJ+XJ <= 850

DB+NB+XB <= 1000

DS+NS+XS <= 1200

XC+XJ+XB+XS >= 920

68DC+79DJ+81DB+58DS >= 65(DC+DJ+DB+DS)

68DC+79DJ+81DB+58DS <= 72(DC+DJ+DB+DS)

89DC+65DJ+78DB+68DS >= 74(DC+DJ+DB+DS)

68NC+79NJ+81NB+58NS >= 77(NC+NJ+NB+NS)

89NC+65NJ+78NB+68NS >= 70(NC+NJ+NB+NS)

89NC+65NJ+78NB+68NS <= 80(NC+NJ+NB+NS)

90NC+77NJ+95NB+59NS >= 80(NC+NJ+NB+NS)

89XC+65XJ+78XB+68XS >= 81(XC+XJ+XB+XS)

90XC+77XJ+95XB+59XS >= 88(XC+XJ+XB+XS)

DC, DJ, DB, DS, NC, NJ, NB, NS, XC, XJ, XB, XS >= 0

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