How do you do a 3 variable linear problem in the easiest manner?

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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