Question

Find the values of x1 and x2 where the following two constraints intersect.

1) 9x1 + 7x2 ≥ 57

(2) 4x1 + 6x2 ≥ 13

Answer 1

`x_1=9.654` and
`x_2=-4.269`

Explanation:

Given :
`9x_1 + 7x_2 \geq 57`

`4x_1 + 6x_2\geq 13`

To Find : Find the values of
`x_1`and
`x_2` where the following two constraints intersect.

Solution:

`9x_1 + 7x_2 \geq 57`

`4x_1 + 6x_2\geq 13`

Plot these constraints on the graph

`9x_1 + 7x_2 \geq 57` --- Red

`4x_1 + 6x_2\geq 13` --- Blue

The intersection point will provide the solution

So, Intersection point = (9.654,-4.269)

So,
`x_1=9.654` and
`x_2=-4.269`

Refer the attached figure .