Question

The graph of a linear programming problem is given below. The shaded region is the feasible region. The objective function is Z = px + qy

1. What are the co-ordinates of the comers of the feasible region.
2. Write the constraints
3. If the Max. Z occurs at A and B, what is the relation between p and q?
4. If q = 1, write the objective function
5. Find the Max Z

Answer 1

1. Corner points are O(0, 0), A(5, 0), B(3, 4), C(0, 5).

2. Constraints are 2x + y ≤ 10, x + 3y ≤ 15, x ≥ 0, y ≥ 0.

3. At (3, 4), Z = 3p + 4q

At (5, 0), Z = 5p

⇒ 3p + 4q = 5p ⇒ p = 2q.

4. If q = 1, p=2

Then the objective function is,

Maximize Z = 2x + y.

5. At (3, 4) Z = 2 × 3 + 4 = 10 is the maximum value.