Question

By graphing the system of constraints find the values of x and y that maximize the objective function, find the maximum value.

Answer 1

P = 4 IS THE ANSWER KKKKKKKKKKKKKKK

Answer 2

Answer:

x=1, y=4

P=6

Step-by-step explanation:

We are given that

$3x+y\leq 7$

$x+2y\leq 9$

$x\geq 0$

$y\geq 0$

Objective function

$P=2x+y$

We have to values of x and y that maximize the P and maximum value of P .

First we change inequality equation into equality equation

$3x+y=7$  (I equation )

$x+2y=9$  (II equation)

Equation I multiply by 2 and then subtract from II equation

$-5x=-5$

$x=1$

Substitute x=1 in equation I

Then, we get

$3(1)+y=7$

$3+y=7$

$y=7-3=4$

The two equation intersect at point (1,4).

Substitute x=0 in equation I

Then , we get y=7

Substitute y=0 then

$3x=7$

$x=\frac{7}{3}=2.3$

The equation I cut the x- axis at point (2.3,0)and y-axis at (0,7).

Substitute x=0 in equtaion II

$2y=9$

$y=\frac{9}{2}=4.5$

Substitute y=0

Then, we get

$x=9$

Therefore, the equation II cut the x- axis at point (9,0) and y axis at point (0,4.5).

Substitute x=0 and y=0 in inequality Equation I

$3(0)+0=0< 7$

It is true . Therefore, shaded region below the line.

Substitute x=0 and y=0 in inequality equation II

Then, $0+2(0)=0 < 9$

It is true. Therefore, the shaded region below the line.

The feasible region is bounded.The feasible region bounded by (0,0),(0,4.5),(2.3,0) and (1,4).

At (0,4.5)

$P=2(0)+4.5=4.5$

At (2.3,0)

$P=2(2.3)+0=4.6$

At (1,4)

$P=2(1)+4=6$

At (0,0)

$P=2(0)+0=0$

Hence, maximum value of P is 6 at (1,4).

x=1 and y=4