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You and your Learning Team are buyers for a coffeehouse and are responsible for purchasing the beans. This month, you must buy three grades of coffee bean. The different grades are blended with various flavors to make well-known coffee drinks. The beans are selling for $0.80, $1.20, and $1.80 per pound. You want to know how much of each grade of bean to buy based on the following assumptions given to you by the owner:
- The total weight of beans needed is 15,000 pounds to minimize shipping costs.
- You must spend the budgeted amount of $20,000.
- You need 2,000 more pounds of the most expensive grade than the least expensive grade.
Provide step-by-step directions and general guidelines for placing a matrix in reduced row echelon form (RREF) using Gauss-Jordan elimination to solve the problem:
- Use x, y, and z to represent the weights of the three grades of beans you buy, where x is the weight of the least expensive bean, y is the weight of the next expensive bean, and z is the weight of the most expensive bean.