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svetlana [45]
3 years ago
13

Graph the system of constraints and find the value of x and y that maximize the objective function.. x>0. y>0. y<1/5x+2

. 5>y+x. objective function: c=7x-3y

Mathematics
2 answers:
Travka [436]3 years ago
5 0
X > 0 , everything to the right of the y-axis 
<span>y > 0 , everything above the x-axis </span>
So far you are in quadrant I of the x-y plane
<span>y<1/5x+2
</span><span>sketch a line leaning 45° to the left with a y-intercept of 2, shade in everything below that line 
</span>now our Objective Function is 
<span>C = 7x - 3y , which is a line with slope 7/3 </span>
<span>letting that line go through the origin, let it slide parallel to itself over the shaded region until you reach the farthest point from the origin. </span><span>
Here are the required values : 
c = 35; x = 5, y = 0</span>
iogann1982 [59]3 years ago
3 0

Answer: The value of x= 5

And the value of y =0.

Step-by-step explanation:

Since we have given that

Max\ c=7x-3y\\\\yy+x\\\\s.t.\  x>0\ y>0

As we can see from the graph, there are three points occurred in feasible region, which are as follows;

A(2.5,2.5)\\\\B(-10,0)\\\\C(5,0)

Now, we put the above three values in the objective function:

c=7x-3y\\\\Put\ A(2.5,2.5)\\\\c=7\times 2.5-3\times 2.5\\\\c=17.5-7.5\\\\c=10\\\\Similarly,\\\\Put\ B(-10,0)\\\\c=7\times -10-3\times 0\\\\c=-70\\\\Similarly,\\\\Put\ C(5,0)\\\\c=7\times 5-3\times 0\\\\c=35

Therefore, we can see that

At C(5,0) we get maximum value as c = 35.

Hence,  The value of x= 5

And the value of y =0.

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Cerrena [4.2K]

Answer:

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Step-by-step explanation:

Product means multiplication

So 9*p equals 9p

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4 0
3 years ago
A biologist has been observing a tree's height. This type of tree typically grows by 0.22 feet each month. Fifteen months into t
Lyrx [107]

Data:

x: number of months

y: tree's height

Tipical grow: 0.22

Fifteen months into the observation, the tree was 20.5 feet tall: x=15 y=20.5ft (15,20.5)

In this case the slope (m) or rate of change is the tipical grow.

m=0.22

To find the line's slope-intercep equation you use the slope (m) and the given values of x and y (15 , 20.5) in the next formula to find the y-intercept (b):

\begin{gathered} y=mx+b \\ 20.5=0.22(15)+b \\ 20.5=3.3+b \\ 20.5-3.3=b \\ 17.2=b \end{gathered}

Use the slope(m) and y-intercept (b) to write the equation:

\begin{gathered} y=mx+b \\  \\ y=0.22x+17.2 \end{gathered}A) This line's slope-intercept equation is: y=0.22x+17.2

B) To find the height of the tree after 29 months you substitute in the equation the x for 29 and evaluate to find the y:

\begin{gathered} y=0.22(29)+17.2 \\ y=6.38+17.2 \\  \\ y=23.58 \end{gathered}Then, after 29 months the tree would be 23.58 feet in height

C) In this case as you have the height and need to find the number of moths you substitute the y for 29.96feet and solve the equation for x, as follow:

\begin{gathered} 29.96=0.22x+17.2 \\ 29.96-17.2=0.22x \\ 12.76=0.22x \\ \frac{12.76}{0.22}=x \\  \\ 58=x \end{gathered}Then, after 58 months the tree would be 29.96feet tall
3 0
1 year ago
Find the measure of
Ann [662]
Find the measure of O?
Line UV is a supplementary line. Line UV is 180 degrees. Angle TU is 30 degrees. Angle WV is 65 degrees. Angle TW (O) is unknown. Add the given angles. 30+65=95 degrees. Subtract the sum of the two angles from 180 degrees. 180-95=85. O is 85 degrees
7 0
3 years ago
Ms. Hamby gave a quiz. Two students' work and the answer key are shown. Ms. Hamby accepts equivalent answers in any form. Part A
Zina [86]

Answer:

attach a picture

Step-by-step explanation:

4 0
3 years ago
During the summer, the height of the water in the pool decreased by 5 inches each week due to evaporation. What is the change in
rjkz [21]

Answer:

40 inches

Step-by-step explanation:

We know that the height of water in a pool decreased 5 inches per week.

This means that we can form the equation y=-5x, since the amount of water remaining is proportionate to the amount of weeks that have passed.

We know x=8, since we need to find the change for 8 weeks.

y = -5\cdot 8

-5 \cdot 8 = -40

y=-40

The change will be the absolute value of -40, which just makes it positive, so 40.

Hope this helped!

8 0
3 years ago
Read 2 more answers
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