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

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 56 students, requires 22 chaperones, and costs $1300 to rent. Each van can transport 88 students, requires 1 chaperone, and costs $110 to rent. Since there are 448 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 448 students. Since only 26 parents have volunteered to serve as chaperones, the officers must plan to use at most 26 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportationcosts? What are the minimal transportation costs?

The officers should rent ____ buses and ____ vans to minimize the transportation costs.The minimal transportation costs are $_________

Solution

Each bus can transport 56 students, requires 22 chaperones, and costs $1300 to rent. Each van can transport 88 students, requires 1 chaperone, and costs $110 to rent

let officers rent x buses and y vans

lets construct a table

                            x                             y

students              56                           88

chaperons           22                            1

cost                  $ 1300                     $110

56x + 88 y >= 448  

22x + 1y <= 26

x , y >= 0

objective function is z = 1300x + 110 y

on graphing the inequalities we get corner points as

( 0,5.091) , (.979,4,468) , (0,26)

checking objective function at each corner point

(0,5.091)

1300x + 110 y = 110(5.091) = $560.01

((.979,4.468)

1300(.979)+110(4.468) = $1387.16

(0,26)

1300(0) + 26(110) = $ 2860

therefore,

0 buses and 5 vans will minimize the transportation cost

minimal cost = $ 560.01