Question

What is y greater then or equal to 2x on a graph

Answer 1

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

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)