1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
9966 [12]
3 years ago
9

A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out st

udent 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.
Clearly state the problem (objective function, constraints)
Mathematics
1 answer:
neonofarm [45]3 years ago
6 0

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

You might be interested in
5(x+4)+16<br><br> Match each of the following with Equivalent Expression listed on the right
son4ous [18]
5(x+4)+16
5x+20+16
And then the solution is 5x+36
6 0
2 years ago
Determine the approximate ordered pair for f(x) = g(x). the graph of two linear functions negative 4 times x plus 15 times y equ
melisa1 [442]

Answer:

  (x, y) ≈ (2.848, -19.241)

Step-by-step explanation:

I find it much easier to work with the problem statement when math expressions are written using numbers and symbols. We assume you have ...

  -4x +15y = -300

  20x +4y = -20

Dividing the second equation by 4 and subtracting the x-term gives ...

  y = -5-5x

Substituting that into the first equation, we get ...

  -4x +15(-5-5x) = -300

  -79x -75 = -300

  x = -225/-79 = 2 67/79 ≈ 2.8481

Substituting this into the equation for y gives ...

  y = -5(x +1) = -5(3 67/79) = -19 19/79 ≈ -19.2405

The approximate solution is ...

  (x, y) = (2.8481, -19.2405)

3 0
3 years ago
Pls help me divide this radical and pls show work
Alenkinab [10]
Let's start by rationalizing the radical:

4√6/√50 * √50/√50

This gets rid of the radical in the denominator, giving us:

4√300/50

√300 can be simplified to √3 * √100 or 10√3. Now we can insert this back into the numerator:

4 * 10√3/50

This is equivalent to:

40√3/50

40/50 can be simplified to 4/5.

Therefore, the answer is 4√3/5.
5 0
3 years ago
Write a linear function f withe the values f (10) = 5 and f (2) = -3​
MakcuM [25]

Answer:

(a) f(x)=\frac{1}{2}x

(b)f(x)=-\frac{3}{2}x

Step-by-step explanation:

8 0
2 years ago
Write the expression as a square of a binomial: 9/25a^6b^2-a^4b^4+25/36a^2b^6
OlgaM077 [116]

answer below,

<h2>Hope this helps :></h2><h2 /><h2>From Cambridge</h2><h2 /><h2>please give brainliest!</h2>

5 0
3 years ago
Other questions:
  • A painter is working on a canvas that has a total area of 338 square inches. The canvas is x inches wide and twice as long as it
    5·2 answers
  • Need some help!!! Simplify: (3x^2y)*(5x^3y^2)
    8·1 answer
  • Find the sum of the first 50 terms of the sequence -6, -2, 2, 6
    9·1 answer
  • 3x + x + 8 = 20 hhhhhhhhhhhssjsjjsjzjsjjsjsjsjsjsjsjsjsjsjjs
    8·1 answer
  • I need help with this fast​
    11·1 answer
  • *PLEASE ANSWER, DIFFICULT QUESTION* Thomas wants to invite Madeline to a party. He has an 80% chance of bumping into her at scho
    15·1 answer
  • Consider (2x – 1) + 2 &gt; x + 1. Use the addition or subtraction
    9·1 answer
  • Which expression is equivalent to 9x − 12?
    7·2 answers
  • Is -3/4 greater or less than or equal-.75
    14·1 answer
  • Step 1: Subtract 3 from both sides of the inequality.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!