A graph represents the feasible region for the system: y is less than or equal to 2x, x + y is greater than or equal to 45, and
x is less than or equal to 30. What is the minimal number for the objective function P = 20x + 16y? What is the value of x then? What is the value at y then?
2 answers:
<h2>Answer:</h2>
- 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
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)
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