Answer:
The minimal number for the objective function P =20x+16y is: 780
The value of x then is: 15
and the value of y then is : 30
Step-by-step explanation:
We are given a system of inequalities as:
y is less than or equal to 2x
i.e.          y ≤ 2x--------(1)
x + y is greater than or equal to 45
i.e.      x+y ≥ 45  ------------(2)    
and    x is less than or equal to 30.    
i.e.               x ≤ 30 -----------(3)    
On plotting these inequalities we get the boundary points as:
         (15,30) , (30,60) and (30,15)    
( Since, the optimal solution always exist at the boundary point )
The optimal function is given by:
 Minimize  P = 20x+16y
Hence, at (15,30) we get:
P= 780
at (30,60) we get:
  P= 1560
at (30,15) we get:
P= 840
This  means that the minimal value of the function is 780
and the value exist at (15,30)