Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 ​people, while each carton of clothing will help 6 people. Each 20​-cubic-foot  box of food weighs 50 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 24,000 pounds.​- The total volume must be no more than 6000 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.

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Asked Feb 9, 2020
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Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 ​people, while each carton of clothing will help 6 people. Each 20​-cubic-foot  box of food weighs 50 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 24,000 pounds.
​- The total volume must be no more than 6000 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.
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Expert Answer

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Step 1

Let x be the number of cartons of food and y be the number of cartons of clothing required. Then, the objective function is,

Algebra homework question answer, step 1, image 1

Step 2

From the given data the following constraints are obtained.

Algebra homework question answer, step 2, image 1

Step 3

Graph the constraints and obtain the corner points.

Algebra homework question answer, step 3, image 1

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