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3 years ago

The graph shows the feasible region for the system with constraints:

Mathematics

2 answers:

Dimas [21]3 years ago

6 0

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

substitute the three vertices of the feasible region in C and chose

the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

nignag [31]3 years ago

5 0

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

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Three times a number x is more than 18.

poizon [28]

Answer:

3x>18

Step-by-step explanation:

Three times the number x will be called 3x. If an expression is more or greater than a number, we use the greater symbol: >

So, we can write,

3x>18

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2 years ago

If the points at (-4, 3) and (2, 3) are reflected over the x-axis to create two new points, what shape can be formed by the four

Svetllana [295]

Answer:

Step-by-step explanation:

Let $(a,b)\in \mathbb{R}^{2}$ , a reflection over the x-axis consists in the following operation:

$(a,b) \rightarrow (a,-b)$

If we know that $X = (-4,3)$ and $Y = (2, 3)$ , then the points translated over the x-axis are $X' = (-4, -3)$ and $Y' = (2,-3)$ , respectively. The most precise description of the shape is a rectangle for the following facts:

1) $XX' = YY' = 8$ and $XY = X'Y' = 6$ .

2) $X$ and $X'$ have the same x-component.

3) $Y$ and $Y'$ have the same x-component.

4) $X$ and $Y$ have the same y-component.

5) $X'$ and $Y'$ have the same y-component.

A representation of the shape is included below as attachment.

3 0

3 years ago

A environmental initiative has the goal of saving at least 25 2525 million hectares of rainforest through both planting trees an

Anestetic [448]

Answer:

The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.

Step-by-step explanation:

Let the variable X represent the amount of land used for planting trees and Y represent the amount of land purchased.

The goal of the environmental initiative is to save at least 25 million hectares of rain forest.

That is:

X + Y = 25....(i)

Now it is provided that:

The cost of planting trees is $ 400 per hectare.
The cost of purchasing land is $ 260 per hectare.
The initiative has a budget of $8,250 million.

Using the above data it can be said that:

400X + 260Y = 8250....(ii)

Solve equations (i) and (ii) simultaneously.

$\ \ \ \ x+y=25]\times 260\\400x+260y=8250\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\\Rightarrow\\\\260x+260y=6500\\400x+260y=8250\\(-)\_\_\_\_\_\ (-)\_\_\_\_(-)\_\_\_\\\\\Rightarrow\\\\-140x=-1750\\\\x=\frac{1750}{140}\\\\x=12.5$

Then the value of y is:

$x+y=25\\y=25-x\\y=25-12.5\\y=12.5$

Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.

4 0

3 years ago

Help, I need to figure this out.

postnew [5]

Your answer would be 45 and 1/3

6 0

2 years ago

Read 2 more answers

Which is an x-intercept of the continuous function in the table?

LiRa [457]

Answer: OPTION A.

Step-by-step explanation: