(2) In a linear programming problem, the binding constraints for the optimal solution are:

5x+3y30

2x+5y20

Which of these objective functions will lead to the same optimal solution? (choose 3)

Group of answer choices

2x+1y

80x+60y

7x+8y

25x+35y

(3)The optimal solution of this linear programming problem is at the intersection of constraints 1 (c1) and 2 (c2).

Max2x1+x2

s.t.4x1+1x2400

4x1+3x2600

1x1+2x2300

x1,x20

Over what range can the coefficient of x1 vary before the current solution is no longer optimal?

Group of answer choices

0.5c11.5

1.45c14.58

1.33c14

3c15

(4)The optimal solution of this linear programming problem is at the intersection of constraints 1 (c1) and 2 (c2).

Max2x1+x2

s.t.4x1+1x2400

4x1+3x2600

1x1+2x2300

x1,x20

Over what range can the coefficient of x2 vary before the current solution is no longer optimal?

None of these

2.5c26

1.33c24

0.5c21.5

(5) The optimal solution of this linear programming problem is at the intersection of constraints 1 (c1) and 2 (c2).

Max2x1+x2

s.t.4x1+1x2400

4x1+3x2600

1x1+2x2300

x1,x20

Compute the dual prices for the three constraints (3 points).

Group of answer choices

0.5, 0.5, and 1

0.25, 0.25, and 0

1.25, 1.50, and 2

0.00, 0.25, and 0.50