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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 ​students, requires ​chaperones, and costs ​$to rent. each van can transport ​students, requires 1​ chaperone, and costs ​$ to rent. since there are students in the senior class that may be eligible to go on the​ trip, the officers must plan to accommodate at least students. since only parents have volunteered to serve as​ chaperones, the officers must plan to use at most 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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### James

Guys, does anyone know the answer?

get the officers of a high school senior class are planning to rent buses and vans for a class trip. each bus can transport ​students, requires ​chaperones, and costs ​$to rent. each van can transport ​students, requires 1​ chaperone, and costs ​$ to rent. since there are students in the senior class that may be eligible to go on the​ trip, the officers must plan to accommodate at least students. since only parents have volunteered to serve as​ chaperones, the officers must plan to use at most chaperones. how many vehicles of each type should the officers rent in order to minimize the transportation​ costs? what are the minimal transportation​ costs? from EN Bilgi.

## The officers of a high school senior class are planning to r

Find step-by-step solutions and your answer to the following textbook question: The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 3 chaperones, and costs $1,200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs$100 to rent. Since there are 400 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 400 students. Since only 36 parents have volunteered to serve as chaperones, the officers must plan to use at most 36 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?.

### Explanation

Verified

Let x = number of buses, y=number of vans rented.

We want to minimize cost,

C= 1200x+100y C=1200x+100y subject to

\left\{\begin{array}{ll} 40x+8y\geq 400 & \text{... students} \\ 3x+y\leq 36 & \text{... chaperones} \end{array}\right.

{ 40x+8y≥400 3x+y≤36 ​ ... students ... chaperones ​ and

x≥0,y≥0.

Graphically solving, (using desmos.com)

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## SOLUTION: The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 72 students, requires 3 chaperones, and costs $1,400 to rent Algebra -> Customizable Word Problem Solvers -> Finance -> SOLUTION: The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 72 students, requires 3 chaperones, and costs$1,400 to rent      Log On

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Source : www.algebra.com

## Problema Solution

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 40 students, requires 4 chaperones, and costs $1,200 to rent. Each van can transport 8 students, requires 1 chaperone, and costs$90 to rent. Since there are 560 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 560 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?

## Answer provided by our tutors

Let x = number of buses y = number of vans the constrains are:

40x + 8y >= 560 (the officers must plan to accommodate at least 560 students)

4x + y <= 60 (only 60 parents have volunteered to serve as chaperones)

x >= 0 y >= 0

click here to see the graph of the above system of inequalities:

Click to see all the steps

the critical points are:

(14, 0) (we get this point by solving the system of equations: 40x + 8y = 560, y = 0)

(15, 0) (we get this point by solving the system of equations: 4x + y = 60, y = 0)

(10, 20) (we get this point by solving the system of equations: 40x + 8y = 560, 4x + y = 60)

the objective function is F(x, y) = 1200x + 90y we need to find the minimum

F(14, 0) = 1200*14 + 90*0 = $16,800 F(15, 0) = 1200*15 + 90*0 =$18,000

F(10, 20) = 1200*10 + 90*20 = $13,800 in order to minimize the transportation costs the officers should rent 10 buses and 20 vans. the minimal transportation costs are$13,800.

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James 3 day ago

Guys, does anyone know the answer?