A company makes products 1 and 2 from two resources. The linear programming model for determining the amounts of product 1 and 2 to produce (i.e. X1 and X2 ) is
Maximize Z = 8x1 + 12x2 (profit, $)
subject to
4x1 + 5x2 ≤ 20 (resource1, lb)
2x1 + 6x2 ≤ 18 (resource2, 2h)
3x1 + 4x2 ≤ 24 (resource3, ft)
X1, X2 ≥ 0
Using the graphical solution method described in class,
a. Plot the constraints to identify the feasible region;
b. Plot two Iso-profit lines to identify the optimal corner point
c. Solve for the primal solution using elimination and back substitution
d. Construct the matrix of detached coefficients
e. Solve for the shadow prices for the binding constraints, including units of measure.