A coffee manufacturer blends three component coffee beans intothree final blends of coffee. The Table below summarizes the veryprecise recipes for the final coffee blends, the cost andavailability information for the three components, and thewholesale price per pound of the final blends. The percentages inthe body of the table indicate the percentage of each component tobe used in each blend.
Table: Percentage of each component to be used in each blend
_____________________________________________________________________________ Final Blend(percent)
CostPer Maximum Availability
Component 1 2 3 Pound Each Week (Pound)
_____________________________________________________________________________
1 80 0 20 $0.60 40,000
2 50 15 35 $0.80 25,000
3 0 40 60 $0.55 20,000
_____________________________________________________________________________
Wholesale Price/lb. $1.25 $1.50 $1.40_____________________________________________________________________________
Weekly capacity for the processor's plant is 100,000 pounds, andthe company wishes to operate at capacity. There is no problem inselling the final blends, although there is a requirement thatminimum production level of 10,000, 25,000 and 30,000 pounds,respectively, be met for blends 1, 2 and 3. The manufacturer wishesto determine the number of pounds of each component to be purchasedso as to maximize total weekly profit.
Formulate the problem as an L.P. model.
