Determine and graph the feasible region

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Reference no: EM13101229

Min 3X + 3Y
s.t. 12X + 4Y ? 48
10X + 5Y ? 50
4X + 8Y ? 32
X , Y ? 0

a. Determine and graph the feasible region.
b. Enumerate (find) the corner points of the feasible region. (Note: not every point where the constraints intersect is part of the feasible region.)
c. Evaluate the objective function at each of the corner points and determine the optimal solution.
d. What is the optimal value?
e. Which constraints are binding?
f. Determine the surplus or excess capacity in the constraints.
g. Keeping c2 (the constant on the decision variable x2) fixed at 3, over what range can the objective coefficient for x1 (c1) vary before there is a change in the optimal solution? [Hint: find the slopes of the lines from the binding constraints. These form the upper and lower bounds on the slope of the objective function.]
h. If the objective function is changed to Min z = 7x1 + 6x2, what will be the optimal solution and objective value?
i. If the objective function, above, is changed to Min z = 6x1 + 3x2, will the linear program above exhibit infeasibility, unboundedness or alternate optimal solutions?

Reference no: EM13101229

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