Answer:
Minimum value of [tex]p=10x+26y[/tex] is 80 at (1.5,2.5)
Step-by-step explanation:
We are given
The objective function is, Minimize [tex]p=10x+26y[/tex]
With the constraints as,
[tex]x+y\leq 6\\5x+y\geq 10\\x+5y\geq 14[/tex]
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 [tex]p=10x+26y[/tex]
(1,5) [tex]p=10x\times 1+26\times 5[/tex] i.e. p = 140
(1.5,2.5) [tex]p=10\times 1.5+26\times 2.5[/tex] i.e. p= 80
(4,2) [tex]p=10\times 4+26\times 2[/tex] i.e. p = 92
Thus, the minimum value of [tex]p=10x+26y[/tex] is 80 at (1.5,2.5).
