Wildcat Coffee Inc., uses four types of coffee beans (Columbia, Java, Brazil, an
ID: 381383 • Letter: W
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 Bean
Cost Per Pound
Caffeine Rating
Taste Ratting
Aroma Rating
Available 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
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:
Coffee Product
Selling Price per Pound
Product Segment
Product Information
Everyday
$2.20
Low Price Segment
Caffeine level rates between 65 to 72; Taste level rates above 74; No Aroma level requirement
Energy
$2.80
High Caffeine Segment
Caffeine level rates above 77; Tastes level rates between 70 and 80; Aroma level rates above 80
Excellence
$3.50
Gourmet Segment
No requirement on the caffeine level; Taste level rates above 81; Aroma level rates above 88
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.
Coffee Bean
Cost Per Pound
Caffeine Rating
Taste Ratting
Aroma Rating
Available 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
Formulation of Linear Programming Problem:
Decision variables:
Objective Function:
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+DJ+DB+DS = 1
NC+NJ+NB+NS = 1
XC+XJ+XB+XS = 1
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)
This constraint is not used in LP formulation - "Due to the popular demand of the gourmet segment, at least 920 pounds of Excellence must be produced", because the availability of coffee beans is not given in the question. Therefore, decision variables are not in terms of quantity, but the proportion of each coffee beans to blend to make each coffee type.
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