By graphing the system of constraints find the values of x and y that maximize the objective function, find the maximum value. 3x+y< =7 x+2y< =9 x> =0 y> =0 maximum for p=2x+y a. p=3 b. p=4 c. p=6 d. p=10

x=1, y=4

P=6

Step-by-step explanation:

We are given that

Objective function

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

 (I equation )

 (II equation)

Equation I multiply by 2 and then subtract from II equation

Substitute x=1 in equation I

Then, we get

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

Substitute x=0 in equation I

Then , we get y=7

Substitute y=0 then

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

Substitute x=0 in equtaion II

Substitute y=0

Then, we get

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

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

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

Then,

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)

At (2.3,0)

At (1,4)

At (0,0)

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

x=1 and y=4