A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:

Student type
Region undergraduate graduate
East $10 $15
Central $12 $18
West $15 $21

The requirements for the survey are as follows:

The survey must have at least 1500 students.
At least 400 graduate students.
At least 100 graduate students should be from the West
No more than 500 undergraduate students should be from the East
At least 75 graduate students should be from the Central region
At least 300 students should be from the West

The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X1 = # of undergraduate students from the East region, X2 = # of graduate students from the East region, X3 = # of undergraduate students from the Central region, X4 = # of graduate students from the Central region, X5 = # of undergraduate students from the West region, and X6 = # of graduate students from the West region.

Required:
Clearly state the problem (objective function, constraints)

Answers

Answer 1

Answer:

Objective Minimize 10x1 +15x2 + 12x3+18x4+15x5+ 21x6

The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.

The total minimum cost would $ 17586 +$260+ $300= $ 18146

Step-by-step explanation:

Let

X1 = # of undergraduate students from the East region,

X2 = # of graduate students from the East region,

X3 = # of undergraduate students from the Central region,

X4 = # of graduate students from the Central region,

X5 = # of undergraduate students from the West region, and

X6 = # of graduate students from the West region.

Then  the cost functions are

y1= 10x1 +15x2

y2= 12x3+18x4

y3= 15x5+ 21x6

According to the given conditions

The constraints are

x1 +x2 + x3+x4+ x5+ x6 ≥ 1500------- A

15X2 +18X4+21X6 ≥ 400---------B

21X6 ≥ 100

X6 ≥ 100/21

X6 ≥ 4.76

Taking

X6= 5

10X1 ≤ 500

X1 ≤ 500/10

X1≤ 5

18X4 ≥ 75

X4 ≥ 75/18

X4 ≥ 4.167

Taking

X4= 5

Putting the values

15X5+ 21X6 ≥ 300

15X5+ 21(5) ≥ 300

15X5+ 105 ≥ 300

15X5 ≥ 300-105

15X5 ≥ 195

X5 ≥ 195/15

X5 ≥ 13

Putting value of X6 and X4 in B

15X2 +18X4+21X6 ≥ 400

15X2 +18(5)+21(5) ≥ 400

15X2 +195 ≥ 400

15X2  ≥ 400-195

15X2  ≥ 205

X2  ≥ 205/15

X2  ≥ 13.67

Taking X2= 14

Now putting the values in the cost equations to check whether the conditions are satisfied.

y1= 10x1 +15x2

y1= 10 (5) + 15(14)= 50 + 210= $ 260

y3= 15x5+ 21x6

y3= 15 (13) + 21(5)

y3= 195+105= $ 300

x1 +x2 + x3+x4+ x5+ x6 ≥ 1500

5+14+x3+5+13+5≥ 1500

x3≥ 1500-42

x3≥ 1458

y2= 12x3+18x4

y2= 12 (1458)  + 18 (5)

y2= 17496 +90

y2= $ 17586

The cost can be minimized if the number of students from

                                 Undergraduate         Graduate

East Region              X1≤ 5                            X2  ≥ 13.67

Central                      X3≥ 1458                   X4 ≥ 4.167

West                          X5 ≥ 13                          X6 ≥ 4.76

This will result in the required number of students that is 1500

Constraints:

East Undergraduate must not be greater than 5

East Graduate must not be less than 13

Central Undergraduate must  be greater than 1458

Central Graduate must  be greater than 4

West Undergraduate must  be greater than 13

West Graduate must  be greater than 4

The central total cost $ 17586 due to the number of central undergraduate students 1458 is very high.

The east region has a least cost of $260 and west region has a cost of $300.

The total minimum cost would $ 17586 +$260+ $300= $ 18146


Related Questions

csc^ 2 theta- csc^ 2 theta sec^ 2

Answers

Answer:

-csc²θ(tan²θ)

Step-by-step explanation:

csc²θ-csc²θ(sec²θ)

-csc²θ(-1+sec²θ)

-csc²θ(tan²θ)

The line shown below has the equation y = 2/3x-1
The highlighted point has coordinates (-4.3).

Answers

Answer:

Step-by-step explanation:

ask cymath it will help you with any mathmatical problem

Question in screenshot

Answers

Answer:

See below

Step-by-step explanation:

[tex]y = {u}^{ \frac{3}{2} } \\ \\ \therefore \: \frac{dy}{du} = \frac{3}{2} {u}^{ \frac{3}{2} - 1 } = \boxed{\frac{3}{2} {u}^{ \frac{1}{2}} } \\ \\ u = 8x + 3 \\ \\ \frac{du}{dx} = 8.1 + 0 = \boxed{8}[/tex]

Suppose that the function y = f(x) is decreasing on the interval ( 5, 7). What can be said about the graph of y= -f(x)

Answers

Since the function y= f(x) is decreasing on the interval (5, 7), y = -f(x) is INCREASING on the interval (5,7), because the slope is inverted due to the negative sign.

The graph of y = -f(x) is increasing on the interval ( 5, 7) if the function y = f(x) is decreasing on the interval ( 5, 7).

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

Suppose that the function y = f(x) is decreasing on the interval ( 5, 7).

The function:

y = -f(x)

Let f(x) be:

f(x) = -aˣ

Here 'a' is the real number a > 0

f(x) is decreasing on the interval ( 5, 7).

Applying transformation:

y = -f(x)

y = aˣ

Function y is increasing on the interval ( 5, 7).

Thus, the graph of y = -f(x) is increasing on the interval ( 5, 7) if the function y = f(x) is decreasing on the interval ( 5, 7).

Learn more about the function here:

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please answer ive been having such a bad day today

Answers

Answer:

A - y = 2x + 1

Step-by-step explanation:

2(2) + 1 = 5

2(4) + 1 = 9

2(6) + 1 = 13

Hope this helps <3

Express 848.41 m in millimeters

Answers

Answer: 848410 millimeters

Move the decimal three places to the right.

A pool in the shape of a rectangular prism has a length of 12 m, a width of 6 m, and a depth of 1.5 m. Find the volume of water needed to fill the pool.

Answers

Answer:

108 m^3

Step-by-step explanation:

The volume of a rectangular prism is the product of all its sides. 12 * 6 * 1.5 = 108

Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H

Answers

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

Answer:

∠A and ∠G

Step-by-Step Explaination:

I did it on

E

D

G

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N

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Is the function shown in the graph one-to-one?


Yes, there exists one input for every output.

No, there exists more than one input for at least one output.

Yes, there exists one output for every input.

No, there exists more than one output for at least one input.

Answers

Yes, there exists one input for every output.

Find a polynomial f(x) of degree 3 that has the following zeros. -1 (multiplicity 2), 8 Leave your answer in factored form

Answers

Answer:

Ganancia neta de la ciencia y dibujos de los gobernante en la vida de las ciudadanos y ciudadanas que ah implementado la Municipalidad de tu distrito para enfrentar la pandemia de mi corazón del gobierno estás a cargo del gobierno estás a cargo

Step-by-step explanation:

Ganancia neta de la ciencia y dibujos de los gobernante en la vida de las ciudadanos y ciudadanas que ah implementado la Municipalidad de tu distrito para enfrentar la pandemia de mi corazón del gobierno estás a cargo

Find mCFD
O 180°
O 276°
O 307°
O 53°

Answers

9514 1404 393

Answer:

  307°

Step-by-step explanation:

The measure of arc CFD is the measure of the whole circle, less the measure of arc CD. The measure of arc CD is the difference between the measures of arc CE and DE. Arc CE has the same measure as arc BF, so we have ...

  arc CFD = 360° -(arc BF -arc ED)

  arc CFD = 360° -132° +79°

  arc CFD = 307°

_____

Arcs BF and CE are of equal measure because their central angles are vertical angles, hence congruent.

Help me pleaseeee thank you

Answers

The answer is D 21t
For each day is an increase of 21

Answer:

D

Step-by-step explanation:

Time is directly proportional to the Cost. And if you use the calculator you'll still get the answer by substituting the time into 21t

Picture Below
(i have to make this 20 characters so I'm doing this now)

Answers

Answer:

H.

Step-by-step explanation:

16x^2 is the big square area and the -10x comes from subtracting the smaller area from the big one

Answer:

H. is the answer

hope this helps

have a good day :)

Step-by-step explanation:

One term of a geometric sequence is a4=135. The common ratio is r=3. Write an explicit rule for the nth term.

Answers

Answer:

[tex]a_{n} = 5 * 3^{n-1}[/tex]

Step-by-step explanation:

To find the nth term of a geometric sequence, you have the general formula:

[tex]a_{1} *r^{n-1}[/tex]

where a1 is the first term and r is the common ratio. In order to find the 4th term, we can substitute what we have(n is 4 because we are looking for the fourth term):

135 = [tex]a_{1} * 3^{4 - 1}[/tex]

135 = [tex]a_{1} * 3^3[/tex]

135 = [tex]27a_{1}[/tex]

[tex]a_{1} = 5[/tex]

Now, we can substitute the first term back in:

[tex]a_{n} = 5 * 3^{n-1}[/tex]

The increasing annual cost (including tuition, room, board, books and fees) to attend college ) to attend college has been widely discussed in many publications including Money magazine. The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.

Private Colleges
53.8 42.2 44.0 34.3 44.0
31.6 45.8 38.8 50.5 42.0

Public Colleges
20.3 22.0 28.2 15.6 24.1 28.5
22.8 25.8 18.5 25.6 14.4 21.8

Required:
a. Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges.
b. What is the point estimate (in thousand dollars) of the difference between the two population means?

Answers

Answer:

a) The sample mean is of 42.7 thousand dollars.

The standard deviation is of 6.38 thousand dollars.

b) The point estimate of the difference between the two population means is of 20.4 thousand dollars.

Step-by-step explanation:

a. Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges.

Sample mean is the sum of all values divided by the number of values. So

[tex]M = \frac{53.8 + 42.2 + 44.0 + 34.3 + 44.0 + 31.6 + 45.8 + 38.8 + 50.5 + 42.0}{10} = 42.7[/tex]

The sample mean is of 42.7 thousand dollars.

Sample standard deviation is the square root of the sum of the difference squared between each number and the mean, divided by the number of values. So

[tex]S = \sqrt{\frac{(53.8-42.7)^2 + (42.2-42.7)^2 + (44.0-42.7)^2 + (34.3-42.7)^2 + (44.0-42.7)^2 + (31.6-42.7)^2 + (45.8-42.7)^2 + (38.8-42.7)^2 + (50.5-42.7)^2 + (42.0-42.7)^2}{10}} = 6.38[/tex]

The standard deviation is of 6.38 thousand dollars.

b. What is the point estimate (in thousand dollars) of the difference between the two population means?

First, we have to find the sample mean for public colleges, and then subtract the sample mean of private colleges by the sample mean of public colleges. So, for public colleges:

[tex]M = \frac{20.3 + 22.0 + 28.2 + 15.6 + 24.1 + 28.5 + 22.8 + 25.8 + 18.5 + 25.6 + 14.4 + 21.8}{12} = 22.3[/tex]

Point estimate of the difference:

42.7 - 22.3 = 20.4

The point estimate of the difference between the two population means is of 20.4 thousand dollars.

42 cubes of side 8cm are packed into a cuboid
64cm by 40cm by 24cm. How many more
cubes are needed to completely fill the cuboid?​

Answers

Answer:

multiply it

Step-by-step explanation:

thats it

A tutoring company would like to understand if most students tend to improve their grades (or not) after they use their services. They sample 220 of the students who used their service in the past year and ask them if their grades have improved or declined from the previous year. Write the null and alternative hypotheses in words.

Answers

Answer:

Null hypothesis :

Grades have not improved for a majority of students

Alternative hypothesis :

Grades have improved for a majority of students

Step-by-step explanation:

The null and alternative hypothesis for this scenario who see the null hypothesis take a midpoint between improvement and decline ; which can be expressed as ;

H0 : p = 0.5

This means that the performance of students is at a centre point where it could swing either way (decline or improve).

To test of grade has improved students, the, the proportion of f students who have proved should be greater. Which is what the test intends.

H1 : p > 0.5

What is the surface area of the sphere below?
5
2.5
A. 1257 units2
B. 1007 units2
C. 12573 units2
O
D. cannot be determined

Answers

Here's the solution :

In a sphere,

[tex] \boxed{ \mathsf{surface \: \: area = 4\pi {r}^{2} }}[/tex]

now, let's solve :

[tex]s = 4 \times \pi \times 5 \times 5[/tex][tex]s = 100\pi[/tex]

hence, correct answer is B. 100π unit²

The surface area of the sphere is 100 π unit².

The correct option is B.

What is Surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

We have,

Radius of Sphere= 5 unit

Now, the formula for Surface area of Sphere is

= 4πr²

= 4 (3.14) (5)(5)

= 4 x 3.14 x 25

= 314

= 10 π unit²

Thus, the Surface area is 10 π unit².

Learn more about Surface area here:

https://brainly.com/question/29101132

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If A = –2p + 7 and B = p2 + 3p – 5, find an expression that equals A – 3B in
standard form.

Answers

Answer:

-3p^2 - 11p + 22

Step-by-step explanation:

A - 3B becomes (-2p + 7) - 3*(p^2 + 3p - 5).

Perform the indicated multiplication, obtaining:

                            (-2p + 7) - 3p^2 - 9p + 15, and then:

                              -2p + 7 - 3p^2 - 9p + 15, or (combining like terms):

                             

                                 -3p^2 - 11p + 22

What is the perimeter of the shape?
- 12 feet
-14 feet
-26 feet
-38 feet

Answers

Answer:

26 ft

Step-by-step explanation:

$5000 grew to $9000 at the compound interest of 12% per annum what was the years taken for the investment​

Answers

Answer:

1year?hehehehehehehehehe

(a) 34 is 85% of what number?

Answers

Answer:

[tex]40[/tex]

hope this helps you.

Can I have the brainliest please?

25 points! Please help!

Answers

Answer: 15 minutes

Explanation:

Answer:

17.5(D)

Step-by-step explanation:

So, lets see:

Every 5 minutes, Raul answers 22 questions.

The test has 77 questions.

We must figure out the time it takes to answer all 77 questions.

To do this, lets first divide the total questions by the questions answered per 5 minutes:

77 / 22

=

3.5

I got 3.5 knowing that 3x22 is 66, and half(0.5) of 22 is 11, and 11 plus 66 is 77.

So, the 3.5 is how many times he answrs 22 questions in five minutes.

To make a bit more sense, basically we have to multiply the 5 minutes by the 3.5:

3.5*5

=

17.5

We know that 3 times 5 is 15. Half(0.5) of 5 is 2.5, so 15+2.5 is 17.5.

So the answer is that for the 77 quesitons, it takes 17.5 minutes

HOPe this helps!

HELP HELP HELP HELP PLZZZZZ

Answers

d bc thats way to much

50 POINTS!!!
Given the point (18, -10), apply the rule and tell the image after the translation as an ordered pair with no spaces.

(x,y) --> (x - 11, y - 9)


[no ridiculous answers or links or i will report]

Answers

Answer:

(7,-19)

Step-by-step explanation:

(x,y) --> (x - 11, y - 9)

Substitute x=18 and y = -10 into the translation

(x,y) --> (18 - 11, -10 - 9)  

             (7,-19)

A circle has radius 6 cm. Suppose an arc on the circle has length 31 cm. Answer the
following:
a. The fraction of the whole circle represented by this arc is
b. The measure of the central angle defined by the arc is
degrees.
C. The area of the sector defined by the arc is
cm2. (Express answer
in terms of r or pi).

Answers

Answer:

[tex]Fraction = \frac{31}{38}[/tex]

[tex]\theta = 296.18^\circ[/tex]

[tex]Area = 29.62 \pi[/tex]

Step-by-step explanation:

Given

[tex]r = 6[/tex]--- radius

[tex]L = 31[/tex] --- arc length

Solving (a): Fraction represented by the arc

First, calculate the circumference (C)

[tex]C = 2\pi r[/tex]

So, we have:

[tex]C = 2 * 3.14 * 6[/tex]

[tex]C = 38[/tex] --- approximated

So, the fraction represented by the arc is:

[tex]Fraction = \frac{L}{C}[/tex]

[tex]Fraction = \frac{31}{38}[/tex]

Solving (b): Measure of the center angle

Using arc length formula, we have:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

This gives

[tex]31 = \frac{\theta}{360} * 2 * 3.14 * 6[/tex]

[tex]31 = \frac{\theta}{360} * 37.68[/tex]

Make [tex]\theta[/tex] the subject

[tex]\theta = \frac{360 * 31}{37.68}[/tex]

[tex]\theta = 296.18^\circ[/tex]

Solving (c): The area of the sector

This is calculated as:

[tex]Area = \frac{\theta}{360} * \pi r^2[/tex]

So, we have:

[tex]Area = \frac{296.18}{360} * \pi * 6^2[/tex]

[tex]Area = \frac{296.18}{360} * \pi * 36[/tex]

Divide 360 and 36

[tex]Area = \frac{296.18}{10} * \pi[/tex]

[tex]Area = 29.618 * \pi\\[/tex]

[tex]Area = 29.62 \pi[/tex] --- approximated

Researchers surveyed 250 college students at one time. They were asked if they were taking any engineering classes and whether or not they felt depressed. If 75 students reported taking at least one engineering class and 15 of those students said they were depressed, what is the incidence of depression in this group

Answers

Answer:

the  incidence of the depression is  1 ÷ 5

Step-by-step explanation:

Given that

There is 250 college students that are surveyed

In the case when 75 students reported for minimum ne engineering class

And, out of this 15 students would be depressed

We need to find out the incidence of the depression

So

= 15 ÷ 75

= 1 ÷ 5

Hence, the  incidence of the depression is  1 ÷ 5

find the vertex of the graph of the following quadratic equations y= -3x^2 -12x-13

Answers

by using the rule -b/2a —> 12/-6= -2

Answer:

Step-by-step explanation:

The vertex is a point. The x value is defined as x = - b / 2a where

a = -3

b = - 12

x = - -12/ 2* -3

x = 12 / - 6

x = -2

what is y when x = - 2?

y = -3(-2)^2 - 12(-2) - 13

y = -12 + 24 - 13

y  = -1

Does the graph agree? It should

The equation is written as

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

Z OO
Which of the following statements are true? Check all that apply
The distance covered on a two hour bloyole ride depende on the bike'e rate of
speed Al 10 mph, the rider will cover 20 miles. Al 18 mph, she will cover 30
miles
A. Distance(16) = 30
B. Distance(30) = 16
C. Distance(20) = 10
D. Distance(10) = 20

Answers

Answer:

Step-by-step explanation:

A. Distance(16)= 30

can anyone help please

Answers

Answer:

x = 0, x = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given

8x² - 12x = 0 ← factor out 4x from each term

4x(2x - 3) = 0

Equate each factor to zero and solve for x

4x = 0 ⇒ x = 0

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

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