Question

The minimum value of z = 10x + 25y subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5 is ______.

विकल्प

• 80

• 95

• 105

• 30

Answer 1

The minimum value of z = 10x + 25y subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5 is 80.

Explanation:

Given, Z = 10x + 25y

and subject to 0 ≤ x ≤ 3, 0 ≤ y ≤ 3, x + y ≥ 5

On taking given constraints as equation, we get the following graph.

Here, intersecting point of lines x = 3 and x + y = 5 is A(3, 2), intersecting point of lines y = 3 and x + y = 5 is B (2, 3} and intersecting point of lines, x = 3 and y = 3 is C(3, 3).

Here, ABCA is the feasible region whose corner points are A(3, 2), ~2, 3) and C(3, 3).

Corner points	Z = 10x + 25y
A(3, 2)	10 × 3 + 25 × 2 = 80  (minimum)
B(2, 3)	10 × 2 + 25 × 3 = 95
C(3, 3)	10 × 3 + 25 × 3 = 105