amount of product 1 = x, amount of product 2 = y, amount of product 3 = z
Milling 9x + 3y + 5z < or = 550
Lathe 5x + 4y + 0z < or = 350
Grinder 3x + 0y + 2z < or = 150
The "easiest" way to solve this is to use a graphing calculator that can do matrices- if that is what you are studying.
Matrix A is a 3 x 3 matrix using the coefficients of the variables in your system.
Matrix B is a 3 x 1 matrix using the answers (constraints) of your system.
Calculate A inverse times B
x = 38 8/9 y = 38 8/9 z = 16 2/3
Or use elimination
Since you can't make fractional amounts round each answer up or down to create the greatest profit.
The possibilities are
x = 39, y = 39, z = 16
x = 39, y = 38, z = 17 (decrease the one with lowest profit)
None of the possibilities that don't make all three products gives a maximum (you can check this)
Profit on the first possibility is
50(39) + 20(39) + 25(16) = $3130
Profit on the second possibility is
50(39) + 20(38) + 25(17) = $3135 best answer