The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 63 students, requires 6 chaperones, and costs $1,100 to rent. Each van can transport 9 students, requires 1 chaperone, and costs $80 to rent. Since there are 567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567 students. Since only 60 parents have volunteered to serve as chaperones, the officers must plan to use at most 60 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 63 students, requires 6 chaperones, and costs $1,100 to rent. Each van can transport 9 students, requires 1 chaperone, and costs $80 to rent. Since there are 567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567 students. Since only 60 parents have volunteered to serve as chaperones, the officers must plan to use at most 60 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.CR: Review Problem Set
Problem 35CR
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 63 students, requires 6 chaperones, and costs $1,100 to rent. Each van can transport 9 students, requires 1 chaperone, and costs $80 to rent. Since there are 567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least
567 students. Since only 60 parents have volunteered to serve as chaperones, the officers must plan to use at most 60 chaperones.
How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?
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