A coffee manufacturer blends three component coffee beans into three final blends of coffee. The Table below summarizes the very precise recipes for the final coffee blends, the cost and availability information for the three components, and the wholesale price per pound of the final blends. The percentages in the body of the table indicate the percentage of each component to be used in each blend.

Table: Percentage of each component to be used in each blend

_____________________________________________________________________________ Final Blend (percent)

Cost Per 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, and the company wishes to operate at capacity. There is no problem in selling the final blends, although there is a requirement that minimum production level of 10,000, 25,000 and 30,000 pounds, respectively, be met for blends 1, 2 and 3. The manufacturer wishes to determine the number of pounds of each component to be purchased so as to maximize total weekly profit.

Formulate the problem as an L.P. model.