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

Answer:

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

Step-by-step 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)