Question

Linear Programming. 20) 3x + y ≤ 7; x + 2y ≤ 9; x ≥ 0; y ≥ 0 Maximize the Objective Function: P = 2x + y show the graph

Answer 1

The value that maximize the objective function is the point (1,4)

Explanation:

we have

`3x+y\leq 7` ----> inequality A

`x+2y\leq 9` ----> inequality B

`x\geq 0` ----> inequality C

`y\geq 0` ----> inequality D

Using a graphing tool

The solution is the shaded area

see the attached figure

The coordinates of the solution area are

`(0,0),(0,4.5),(1,4),(2.33,0)`

we have

The Objective Function is equal to

`P=2x+y`

To find out the value of x and y that maximize the objective function, substitute each ordered pair of the vertices in the objective function and then compare the results

For (0,0) -------->
`P=2(0)+0=0`

For (0,4.5) -------->
`P=2(0)+4.5=4.5`

For (1,4) -------->
`P=2(1)+4=6`

For (2.33,0) -------->
`P=2(2.33)+0=4.66`

The value that maximize the objective function is the point (1,4)