If a maximization problem has an objective function of 3x₁ + 2x₂,which of the following corner points is the optimal solution? A)(0,2) B)(0,3) C)(3,3) D)(5,1) E)(0,0)

Question

Quizplus · Accepted Answer

To find the optimal solution in a linear programming problem, we need to evaluate the objective function at each of the corner points and choose the point that gives the highest value.

Evaluating the objective function at each of the corner points:

- (0,0): 3(0)(1)(1)(0) + 2(0)(1)(2)(0) = 0 
- (0,2): 3(0)(1)(1)(2) + 2(0)(1)(2)(2) = 0 
- (0,3): 3(0)(1)(1)(3) + 2(0)(1)(2)(3) = 0 
- (3,3): 3(3)(1)(1)(3) + 2(3)(1)(2)(3) = 33 
- (5,1): 3(5)(1)(1)(1) + 2(5)(1)(2)(1) = 25

The point (5,1) gives the highest value of 25, which means it is the optimal solution.

If a Maximization Problem Has an Objective Function of 3x1

If a Maximization Problem Has an Objective Function of 3x₁