The minimum and maximum values of the objective function, Z = 5x + 10y subject to the constraints `x +2yle 120, x+y ge 60, x -2y ge 0 , x,y le 0` are respectively

Options

A. 300 and 500
B. 600 and 700
C. 600 and 700
D. 300 and 400

Answer

B

Explanation

Given, problem is to minimise and maximise
Z=5x+10 y
Subject to the constriants,
` x+ 2y le 120, x + y ge 60 `
` x -2y ge 0 and x,y ge 0`

The feasible region is ABCDA, whose corner points are A(60, 0), 8(120, 0), C(60, 30) and 0(40, 20). The values of Z at these points are as follows:

The minimum value of Z is 300 at (60, O) and the m·aximum value of Z is 600 at all the points on the line segment joining the points B (120, 0) and C (60, 30).