I already got the answers but wanna check them before i submit my answers :)
A theater is presenting a program about drinking and driving for students and their parents. The proceeds will be donated to a local alcohol information center. Admission is $14 for parents and $7 for students. However, the situation has two constraints: The theater can hold no more than 180 people and every 2 parents must bring at least 1 student. How many parents and students should attend to raise the maximum amount of money?
and...
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 12 people, while each carton of clothing will help 5 people. Each 20-cubic-foot box of food weighs 50 pounds and each 5-cubic-foot box of clothing weighs 25 pounds. The commercial carries transporting food and clothing are bound by the following constraints:
-The total weight per carrier can not exceed 22,000 pounds.
- The total volume must be no more than 6000 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?
Thanks guys
A theater is presenting a program about drinking and driving for students and their parents. The proceeds will be donated to a local alcohol information center. Admission is $14 for parents and $7 for students. However, the situation has two constraints: The theater can hold no more than 180 people and every 2 parents must bring at least 1 student. How many parents and students should attend to raise the maximum amount of money?
and...
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 12 people, while each carton of clothing will help 5 people. Each 20-cubic-foot box of food weighs 50 pounds and each 5-cubic-foot box of clothing weighs 25 pounds. The commercial carries transporting food and clothing are bound by the following constraints:
-The total weight per carrier can not exceed 22,000 pounds.
- The total volume must be no more than 6000 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?
Thanks guys
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For the first problem, you'll want to have as many parents as possible because they provide the largest amount of money. Because of this, and the fact that for every 2 parents there must be one student, two thirds of the group will be parents.
180 / 3 = 60
Students are 1/3, so 60 (1) = 60 students
Parents are 2/3, so 60 (2) = 120 parents
120($14) + 60($7) = $2100
For the second problem, I'm assuming everyone must be fed and clothed. Because of this, an equal amount of supplies must be dispersed. The best way I know of would be to find the least common multiple of 12 and 5 (which is 40) and multiple each amount of food and clothing by the necessary number to reach 40 (5 for food, 12 for clothing)
5(20 cubic feet) and 5(50 pounds) = 100 cubic feet and 250 pounds of food per 40 people
12(5 cubic feet) and 12(25 pounds) = 60 cubic feet and 300 pounds of clothing per 40 people
After adding you'll get 160 cubic feet and 550 pounds per 40 people.
Divide 160 into 6000 to get 37.5, which becomes 37 because you aren't trying to supply half a person.
Divide 550 into 22,000 to get 40.
The answer is 37, because the volume limit is reached before the weight limit is.
180 / 3 = 60
Students are 1/3, so 60 (1) = 60 students
Parents are 2/3, so 60 (2) = 120 parents
120($14) + 60($7) = $2100
For the second problem, I'm assuming everyone must be fed and clothed. Because of this, an equal amount of supplies must be dispersed. The best way I know of would be to find the least common multiple of 12 and 5 (which is 40) and multiple each amount of food and clothing by the necessary number to reach 40 (5 for food, 12 for clothing)
5(20 cubic feet) and 5(50 pounds) = 100 cubic feet and 250 pounds of food per 40 people
12(5 cubic feet) and 12(25 pounds) = 60 cubic feet and 300 pounds of clothing per 40 people
After adding you'll get 160 cubic feet and 550 pounds per 40 people.
Divide 160 into 6000 to get 37.5, which becomes 37 because you aren't trying to supply half a person.
Divide 550 into 22,000 to get 40.
The answer is 37, because the volume limit is reached before the weight limit is.
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Actually, I just realized a step forgot to take on the second problem - you'll need to multiply 37 by 40 to determine the amount of people who will actually be helped - the 37 was simply the amount of boxes you could fit into the plane.
The actual answer comes out to be 1480.
The actual answer comes out to be 1480.
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