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The objective function, z=4x(1)+5x(2), s...

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

A

on X-axis

B

on Y-axis

C

at the origin

D

on the line parallel to X-axis

Text Solution

Verified by Experts

The correct Answer is:
A
Given objective function is
minimise, ` = 4x_(1) +5x_(2)`
Subject of constraints, `2x_(1) + x_(2) ge 7`,
`x_(2) le 3` and `x_(1)x_(2) ge0`
Table for line `2x_(1)+x_(2) = 7s` is


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