1. solve the system using an augmented matrix. show all work. {-x-3y=-17 {2x-6y=-26 2. what point in the feasible region maximizes the objective function? show all work. {x > = 0 {y > = 0 constraints {-x+3 > = y y < = 1/3x +1 3. find the maximum values of x and y that maximize the objective function p = 3x + 2y for the graph. what is the maximum value? show all work. (see image attached for graph! ) 4. what is the solution to the following system of equations? show all work. {3x + 2y + z =7 {5x + 5y + 4z = 3 {3x + 2y + 3z = 1

ANSWER TO QUESTION 1

The augmented matrix is

We use ro operation to solve the above matrix.

The matrix is now in reduce row echelon form

This implies that,

ANSWER TO QUESTION 2

The feasible region is the region satisfied by all the inequalities.

We graph the last two inequalities by graphing their corresponding linear equations and testing the origin for all. We then obtain the feasible region as shown in the attachment.The vertices of the feasible region are:

ANSWER TO QUESTION 3

Given the objective function

We plug in all the vertices of the feasible region to determine the maximum value.

For , we have

For , we have

For , we have

For , we have

Hence the maximum value is 9 and it occurs at

ANSWER TO QUESTION 4

We have the system of equations

We substitute equation (1) in to equation (2) and (3)

Also equation (1) in (3)

We now solve equation 4 and 5 simultaneously.

We multiply equation (4) by 2 and equation (5) by 3

We subtract equation (6) from (7)

We plug in in (5) to find y.

We plug in  and

in (1) to find z.

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step-by-step explanation:

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step-by-step explanation:

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