Mrs. Olsen, a coffee processor, markets three blends of coffee. They are; Brand X , Minim and Taster's Reject. Olsen uses two types of coffee beans to make the three different brands; Columbian and Mexican Beans. The following chart list the composition of the blends:
|
Brand
|
Percentage of Columbian Beans
|
Percentage of Mexican Beans
|
|
Brand X
|
80%
|
20%
|
|
Minim
|
50%
|
50%
|
|
Tasters Reject
|
30%
|
70%
|
Ms. Olsen has already purchased 20,000 pounds of Columbian beans at 90 cents per pound, and she has purchased 30,000 pounds of Mexican beans at 50 cents per pound.
At such, these resources are available for use. Unused Columbian beans can be sold at cost to another processor, but unused Mexican beans can be sold only for 35 cents per pound. Due to warehouse space limitations, Ms. Olsen must dispose of all unused beans.
Brand X sells for $2.60 per pound, Minim sells for $2.50 per pound, and Taster's Reject brings $2.34 per pound. All three products have the same production and packaging costs of $1.20 per pound.
Ms. Olsen is interested in finding the production schedule that will maximize profit. Formulate a relevant linear programming (not integer) model or this problem to maximize profit and determine the solution.