2. Minimization case Consider the following linear programming model for a farmer purchasing fertilizer: minimize Z = $6x1 + 3x2 subject to 2x1 + 4x2 2 16 lb. of nitrogen 4x1 + 3x2 2 24 lb. of phosphate where *1 = bags of Super-gro fertilizer x2 - bags of Crop-quick fertilizer Z = farmer's total cost ($) of purchasing fertilizer This model is transformed into standard form by subtracting surplus variables from the two 2 constraints as follows: minimize Z = 6x1 + 3x2 + 0s, + 0sz subject to 2x1 + 4x2 - 51 = 16 4x1 + 3x2 - $2 = 24 X1,*2, $1, $2 2 0 Use Artificial variables :are assigned a large cost in the objective function to eliminate them from the final solution a. Find the optimal number of super- gro fertilizer(x1) and crop quick fertilizer (x2), and farmers total cost