Question

What is the maximum value of the objective function, P, with the given constraints?

P=20x+35y


x+y≤12
5x+y≤20
x≥0
y≥0




80

390

420

700

Answer 1

420

Explanation:

Answer 2

Option C - 420

Explanation:

Given : Objective function, P, with the given constraints

`P=20x+35y`

Constraints,

`x+y \leq 12`

`5x+y \leq 20\\x \geq 0\\y \geq 0`

To find : What is the maximum value

Solution :

First we plot the graph through the given constrains.

As they all move towards the origin the common region of the equations is given by the points (0,0), (0,12), (2,10), (4,0)

Refer the attached figure.

So, we put all the points in P to, get maximum value.

`P=20x+35y`

• Point (0,0)

`P=20(0)+35(0)=0`

`P=20x+35y`

• Point (0,12)

`P=20(0)+35(12)=420`

• Point (2,10)

`P=20(2)+35(10)=40+350=390`

• Point (4,0)

`P=20(4)+35(0)=80`

Therefore, The value is maximum 420 at (0,12)

So, Option C is correct.