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

Answer:

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

Step-by-step 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)                                  $p=10x\times 1+26\times 5$         i.e. p = 140

(1.5,2.5)                            $p=10\times 1.5+26\times 2.5$    i.e. p= 80

(4,2)                                 $p=10\times 4+26\times 2$          i.e. p = 92

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