hugbug2554

hugbug2554

09.03.2021 •

Mathematics

Mathematical abilities assessment Which assessment are you taking

Solved

Show answers

Ответ:

angie07253

22.04.2022

ANSWER TO QUESTION 1

The augmented matrix is

$\left[\begin{array}{ccc}-1&-3|&-17\\2&-6|&-26\end{array}\right]$

We use ro operation to solve the above matrix.

$-1 \times R1$

$\left[\begin{array}{ccc}1&3|&17\\2&-6|&-26\end{array}\right]$

$R_2-2R_1\rightarrow R_2$

$\left[\begin{array}{ccc}1&3|&17\\0&-12|&-60\end{array}\right]$

$-\frac{1}{12} R_2\rightarrow R_2$

$\left[\begin{array}{ccc}1&3|&17\\0&1|&5\end{array}\right]$

$R_1-3R_2 \rightarrow R_1$

$\left[\begin{array}{ccc}1&0|&2\\0&1|&5\end{array}\right]$

The matrix is now in reduce row echelon form

This implies that,

x=2,y=5

ANSWER TO QUESTION 2

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

$x\ge 0$

$y\ge 0$

$-x+3\ge y$

$y\le \frac{1}{3}x+1$

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:

A(0,1),B(1'5,1.5),C(0,0), D(3,0)

ANSWER TO QUESTION 3

Given the objective function

P(x,y)=3x+2y

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

For A(0,1) , we have

P(0,1)=3(0)+2(1)

P(0,1)=0+2

P(0,1)=2

For B(1.5,1.5) , we have

P(1.5,1.5)=3(1.5)+2(1.5)

P(1.5,1.5)=4.5+3

P(1.5,1.5)=7.5

For C(0,0) , we have

P(0,0)=3(0)+2(0)

P(0,0)=0+0

P(0,0)=0

For D(3,0) , we have

P(3,0)=3(3)+2(0)

P(3,0)=9+0

P(0,1)=9

Hence the maximum value is 9 and it occurs at (3,0)

ANSWER TO QUESTION 4

We have the system of equations

3x+2y+z=7

$\Rightarrow z=7-3x-2y---(1)$

5x+5y+4z=3---(2)

3x+2y+3z=1---(3)

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

5x+5y+4(7-3x-2y)=3

5x+5y+28-12x-8y=3

7x+3y=25----(4)

Also equation (1) in (3)

3x+2y+3(7-3x-2y)=1

3x+2y+21-9x-6y=1

3x+2y=10---(5)

We now solve equation 4 and 5 simultaneously.

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

9x+6y=30---(6)

14x+6y=50----(7)

We subtract equation (6) from (7)

5x=20

$\Rightarrow x=4$

We plug in x=4 in (5) to find y.

3(4)+2y=10

12+2y=10

2y=-2

y=-1

We plug in x=4 and y=-1

in (1) to find z.

$\Rightarrow z=7-3(4)-2(-1)$

$\Rightarrow z=-3$

1. solve the system using an augmented matrix. show all work. {-x-3y=-17 {2x-6y=-26 2. what point in

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice