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Sindrei [870]
3 years ago
11

The number of acres a farmer uses for planting pumpkins will be at least 2 times the number of acres for planting corn. The diff

erence between the acres of pumpkin and corn crops will not exceed 10. He will plant between 12 and 18 acres of pumpkins. The profit for each acre of corn is $225 and the profit for each acre of pumpkins is $360.
A) Write the constraints for the situation. Let x be the number of acres of corn and let y be the number of acres of pumpkins.

B) Write the objective function for the situation.

C) Graph the feasible region. Label the vertex points with their coordinates.

D) How many acres of each crop should the farmer plant to maximize the profit? How much is that profit?

Mathematics
1 answer:
jeka943 years ago
7 0

Answer:

Step-by-step explanation:

A) Let x represent acres of pumpkins, and y represent acres of corn. Here are the constraints:

  x ≥ 2y . . . . . pumpkin acres are at least twice corn acres

  x - y ≤ 10 . . . . the difference in acreage will not exceed 10

  12 ≤ x ≤ 18 . . . . pumpkin acres will be between 12 and 18

  0 ≤ y . . . . . the number of corn acres is non-negative

__

B) If we assume the objective is to maximize profit, the profit function we want to maximize is ...

  P = 360x +225y

__

C) see below for a graph

__

D) The profit for an acre of pumpkins is the highest, so the farmer should maximize that acreage. The constraint on the number of acres of pumpkins comes from the requirement that it not exceed 18 acres. Then additional profit is maximized by maximizing acres of corn, which can be at most half the number of acres of pumpkins, hence 9 acres.

So profit is maximized for 18 acres of pumpkins and 9 acres of corn.

Maximum profit is $360·18 +$225·9 = $8505.

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I have 345 students and I need to fit them all into chairs. However, there are some requirements my seating plan has to keep to:
sveta [45]

In each row, the 15 number of the student is arranged. For the given condition, the equal number of the student is to be arranged.

<h3>What is seating arrangement?</h3>

A seating arrangement is an arrangement shows that how the peoples are arranged so that the complete utilization is done.

The given data in the problem is;

The total no of student is 345 students

If the same number of the students are to be arranged for the given row, the following calculation is done;

The numbers of the student in each row is found as;

\rm  n= \frac{Total \ no \ of \ student\ }{Total\ no \of \ rows } \\\\\ n= \frac{345}{23} \\\\ n= 15 \ student

Hence, in each row, the 15 no of the student is arranged.

To learn more about the seating arrangement, refer to the link;

brainly.com/question/13492666

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3 0
2 years ago
3z+8=20<br> Answer <br> 4<br> 10<br> 8<br> 13
yan [13]

Answer: z = 4

Step-by-step explanation:

3z = 20 - 8

3z = 12

z = 12/3

z = 4

Hope this helped!

7 0
2 years ago
. A triangle has vertices on a coordinate grid at points J(-1, 5), K(4, 5), and L(4, -2). What is the length, in units, of ?
Neko [114]

Answer:

20.6

Step-by-step explanation:

Given data

J(-1, 5)

K(4, 5), and

L(4, -2)

Required

The perimeter of the traingle

Let us find the distance between the vertices

J(-1, 5) amd

K(4, 5)

The expression for the distance between two coordinates is given as

d=√((x_2-x_1)²+(y_2-y_1)²)

substitute

d=√((4+1)²+(5-5)²)

d=√5²

d= √25

d= 5

Let us find the distance between the vertices

K(4, 5), and

L(4, -2)

The expression for the distance between two coordinates is given as

d=√((x_2-x_1)²+(y_2-y_1)²)

substitute

d=√((4-4)²+(-2-5)²)

d=√-7²

d= √49

d= 7

Let us find the distance between the vertices

L(4, -2) and

J(-1, 5)

The expression for the distance between two coordinates is given as

d=√((x_2-x_1)²+(y_2-y_1)²)

substitute

d=√((-1-4)²+(5+2)²)

d=√-5²+7²

d= √25+49

d=  √74

d=8.6

Hence the total length of the triangle is

=5+7+8.6

=20.6

4 0
2 years ago
Which of the following numbers has the commas in the correct positions
Genrish500 [490]
BBB because it has commas after the right units
6 0
3 years ago
A large nest of recently hatched bald eagles is located at the top of the Eiffel Tower (which is 324 meters tall) and is attract
Mariulka [41]

9514 1404 393

Answer:

  80.5°

Step-by-step explanation:

The applicable trig function is the tangent.

  Tan = Opposite/Adjacent

In this scenario, the side opposite the angle is the tower height, 324 m. The side adjacent is the distance to the tower, 54 m. Then the angle α is related by ...

  tan(α) = 324/54

The value of the angle with this tangent is found using the arctangent function:

  α = arctan(324/54) ≈ 80.5°

She should set her binoculars to 80.5°.

6 0
2 years ago
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