Question

A school prepares a field work in which 350 people will participate (among students, representatives, teachers and professors). The transport company has 8 buses with 32 seats and 10 buses with 54 seats. The rental of a large bus costs Bs. 1,080, and a medium one, Bs. 640. How many buses of each type must be rented so that the cost of the tour is the minimum? How much would the transportation cost for the field work?

(A) Bs. 4,480
(B) Bs. 11,880
(C) Bs. 16,360
(D) Bs. 20,840

Answer 1

To minimize the cost of the tour, we need to find the optimal number of buses of each type to rent. The optimal solution is x = 4 and y = 27, which gives a minimum cost of Bs. 16,360. Therefore, the transportation cost for the field work is Bs. 16,360.

Step-by-step explanation:

To minimize the cost of the tour, we need to find the optimal number of buses of each type to rent.

Let's assume we rent x large buses and y medium buses.

The total number of seats in the large buses is 8x, and the total number of seats in the medium buses is 10y.

We need to satisfy the condition that the total number of seats is greater than or equal to 350.

Therefore, 8x + 10y ≥ 350.

To minimize the cost, we want to minimize the number of buses rented.

The cost of renting a large bus is Bs. 1,080, and the cost of renting a medium one is Bs. 640.

Let's define the cost C in terms of x and y: C = 1080x + 640y.

The problem is now to minimize C subject to the constraint 8x + 10y ≥ 350.

We can solve this problem using a linear programming technique called the Simplex Method. The optimal solution is x = 4 and y = 27, which gives a minimum cost of Bs. 16,360.

Therefore, the transportation cost for the field work is Bs. 16,360.