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
jolli1 [7]
3 years ago
8

Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 ​people, while each carton of c

lothing will help 6 people. Each 20​-cubic-foot box of food weighs 40 pounds and each 5​-cubic-foot box of clothing weighs 25 pounds. The commercial carriers transporting food and clothing are bound by the following​ constraints:- The total weight per carrier cannot exceed 21 000 pounds.- The total volume must be no more than 7000 cubic feet.How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?

Mathematics
1 answer:
lutik1710 [3]3 years ago
7 0

Answer:

  233 cartons of food; 467 cartons of clothing

Step-by-step explanation:

This linear programming problem can be formulated as two inequalities (in addition to the usual constraints that the variables be non-negative). One of these expresses the constraint on weight. Let f and c represent numbers of food and clothing containers, respectively.

  40f +25c ≤ 21000

The other expresses the limit on volume.

  20f + 5c ≤ 7000

_____

<u>Feasible Region vertex</u>

We can subtract the boundary line equation of the first inequality from that of 5 times the second to find f:

  5(20f +5c) -(40f +25c) = 5(7000) -21000

  60f = 14000

  f = 233 1/3

The second boundary line equation can be rearranged to find c:

  c = 1400 -4f = 466 2/3

The nearest integer numbers to these values are ...

  (f, c) = (233, 467)

The other vertices of the feasible region are associated with one or the other variable being zero: (f, c) = (0, 840) or (350, 0).

<u>Check of Integer Solution</u>

Trying these in the constraint inequalities gives ...

  • 40·233 +25·467 = 20,995 < 21000
  • 20·233 +5·467 = 6995 < 7000

<u>Selection of the Answer</u>

The answer to the question will be the feasible region vertex that maximizes the number of people helped. That is, we want to maximize ...

  p = 13f + 6c

The values of p at the vertices are ...

  p = 13·233 + 6·467 = 5831

  p = 13·0 + 6·840 = 5040

  p = 13·350 + 6·0 = 2100

The most people are helped when the plane is filled with 233 food cartons and 467 clothing cartons.

You might be interested in
Please solve this for me i dont understand and i will be very appreciative
vredina [299]

Answer: b is for ░▒▓█ Ř █▓▒░

Step-by-step explanation:

5 0
3 years ago
a bus is full of passengers. if you count them by either twos, threes, or fives, there is one left. if you count them by seven t
devlian [24]

Answer:

91.

Step-by-step explanation:

The least number will be a multiple of 7 while the number - 1 will be a multiple of 2,3 and 5.

2*3*5 = 30  but 31 is not a multiple of 7.

2*2*3*5 = 60 but 61  is not divisible by 7.

2*3*3*5 = 90 and 91 is divisible by 7.

3 0
3 years ago
Ausgtin has 1/4 as many cards as mateo. mateo has 1/2 as many cards of amaro. who has the most cards
Nataly [62]

Answer:D

Step-by-step explanation:

Amaro would have the most.

4 0
2 years ago
James has $32 and earns $10 per week for his allowance. What is the initial value for the scenario described? A.10 B.32 C.42 D.3
vova2212 [387]
I think it'll be 32$ cuz thats what he started with.
4 0
3 years ago
Read 2 more answers
PHOTO ATTACHED, please help ASAP, will give brainliest
Svetradugi [14.3K]

Answer: <u>x=11</u>

Step-by-step explanation:

Set the two equations equal to each other

5x+9 = 6x-2

9=x-2

11=x

x=11

X will need to be 11 in order to make the two equations equal to each other

3 0
2 years ago
Other questions:
  • every three days Seth goes to the grocery store every brain goes to the store every 5 days what day will they both go
    10·2 answers
  • What decimal is greater 126.698 or 126.689?
    9·1 answer
  • I can’t figure out how to get this answer.
    7·1 answer
  • 4-x/2=6 solve for x. <br><br><br> jkjhjk
    5·2 answers
  • If f(x) = 2x - 6 and g(x) = 3x + 9, find (f + g)(x)
    12·1 answer
  • what is the smallest number of integer kilogram weights needed to weigh every whole kilogram between 1kg and 40kg?​
    8·1 answer
  • Point B is a point of tangency. Find the radius r of OC.<br> А 9<br> B<br> r<br> n
    8·1 answer
  • A) -8<br> B) 0<br> C) 1 o/ 2 1 over 2 <br> D) 8
    7·2 answers
  • ASAP
    8·2 answers
  • Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish i
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!