The objective function, `z=4x_(1)+5x_(2),` subject to `2x_(1)+x_(2)ge7,2x_(1)+3x_(2)le15,x_(2)le3,x_(1),x_(2)ge0` has minimum value at the point

Options

A. On X-axis
B. on Y-axis
C. at the origin
D. on the line parallel to X-axis

Answer

A

Explanation

Given objective function is
minimise, `z=4x_(2)+5x_(2)`
sujbect of constraints, `2x_(1)+x_(2)ge7`,
`2x_(1)+3x_(2)le15`,
`x_(2) le 3`
and `x_(1),x_(2)ge0`
Table for line `2x_(1)+x_(2)=7` is
`{:(x_(1),0,1,2,3),(x_(2),7,5,3,1):}`
Table for line `2x_(1)+3x_(2)=15`
`{:(x_(1),0,3,6),(x_(2),5,3,1):}`

Now, the value of z at coner points are given below:

Hence, the minimum value of z is 14 at (3.5,0) i.e., at X-axis.