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.

CANT USE EXCEL

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

Solution:

Decision variable:

Let

DC indicate the pounds of Columbia beans used to produce Everyday coffee

DJ indicate the pounds of Java beans used to produce Everyday coffee

DB indicate the pounds of Brazil beans used to produce Everyday coffee

DS indicate the pounds of South Africa beans used to produce Everyday coffee

NC indicate the pounds of Columbia beans used to produce Energy coffee

NJ indicate the pounds of Java beans used to produce Energy coffee

NB indicate the pounds of Brazil beans used to produce Energy coffee

NS indicate the pounds of South Africa beans used to produce Energy coffee

XC indicate the pounds of Columbia beans used to produce Excellence coffee

XJ indicate the pounds of Java beans used to produce Excellence coffee

XB indicate the pounds of Brazil beans used to produce Excellence coffee

XS indicate the 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.

DC+NC+XC <= 700

DJ+NJ+XJ <= 850

DB+NB+XB <= 1000

DS+NS+XS <= 1200

NC+NJ+NB+NS = 1

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)

All variables >= 0

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