Write a system of equations, and solve using either rref or the inverse matrix method. (Show the matrix (matrices) you enter into the calculator , the answer matrix, and the value of each variable.)
The Snack Shop makes three mixes of nuts. Mix A contains 7 pounds of peanuts, 5 pounds of cashews, and 1 pound of pecans.
Mix B contains 3 pounds of peanuts, 2 pounds of cashews, and 2 pounds of pecans. Mix C contains 4 pounds of peanuts, 3 pounds of cashews, and 3 pounds of pecans. The shop has 67 pounds of peanuts, 48 pounds of cashews, and 32 pounds of pecans in stock. How many of each mix can it produce?