Food and clothing are shipped to victims of a natural disaster. Each carton of f
ID: 3111822 • Letter: F
Question
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 11 people, while each carton of clothing will help 5 people. Each 25-cubic-foot box of food weighs 50 pounds and each 5-cubic-foot box of clothing weighs 20 pounds. The commercial carriers transporting food and clothing are bound by the following constraints: The total weight per carrier cannot exceed 22000 pounds. The total volume must be no more than 8000 cubic feet. Use this information to answer the following questions. How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped? The number of cartons of food is __ cartons. The number of cartons of clothing is __ cartons.Explanation / Answer
Let's set x = cartons of food, and y = cartons of clothing.
We know that the total weight has to be less than or equal to 22000 pound.
You wrote that each box of food weights 50 pounds, so we have 50x (since we set x=cartons of food).
And each box of clothing weights 20 pounds, so we have 20y.
Therefore, we should have the following first inequality:
50x+20y 22000
We also have a limit on volume, which is no more than 7000 cubic feet.
Since each box of food is 25 cubic feet, we have 25x. and we have 5y for clothing.
The second inequality should be the following:
25x+5y8000
Then you solve the inequalities by graphing. After you graph, you are interested in finding the maximum of people you can help. You can help 11 people with each box of food (11x) and 5 people with each box of clothing (5y).
objective function
p = 11x + 5y
using simplex method
ableau #1
x y s1 s2 p
25 5 1 0 0 8000
50 20 0 1 0 22000
-11 -5 0 0 1 0
Tableau #2
x y s1 s2 p
1 0.2 0.04 0 0 320
0 10 -2 1 0 6000
0 -2.8 0.44 0 1 3520
Tableau #3
x y s1 s2 p
1 0 0.08 -0.02 0 200
0 1 -0.2 0.1 0 600
0 0 -0.12 0.28 1 5200
Tableau #4
x y s1 s2 p
12.5 0 1 -0.25 0 2500
2.5 1 0 0.05 0 1100
1.5 0 0 0.25 1 5500
from table
Optimal Solution: p = 5500
; x = 0,
y = 1100
Answer:
to help maximum number of people
we need to send
the number of cartoon of clothing x = 0 cartons
the number of cartoon of clothing y = 1100 cartons