Question

find the minimum value of p=10x+26y the constraints are x+y less than or equal to 6, 5x+y greater than or equal to 10, x+5y greater than or equal to 14

Answer 1

Minimum value of
`p=10x+26y` is 80 at (1.5,2.5)

Explanation:

We are given

The objective function is, Minimize
`p=10x+26y`

With the constraints as,

`x+y\leq 6\\5x+y\geq 10\\x+5y\geq 14`

So, upon plotting the constraints, we see that,

The boundary points of the solution region are,

(1,5), (1.5,2.5) and (4,2).

So, the minimum values at these points are,

Points
`p=10x+26y`

(1,5)
`p=10x* 1+26* 5` i.e. p = 140

(1.5,2.5)
`p=10* 1.5+26* 2.5` i.e. p= 80

(4,2)
`p=10* 4+26* 2` i.e. p = 92

Thus, the minimum value of
`p=10x+26y` is 80 at (1.5,2.5).