Consider the following Linear Programming Problem: A school district is buying new buses to transport students in Winnipeg. There are two types of buses available: the Bronco buses and the Neon buses. Each Bronco bus costs 18,000 dollars has a capacity of 25 passengers, and will require 2 mechanical repairs per year. Each Neon bus costs 22,000 dollars has a capacity of 30 passengers, and will require 1 mechanical repair per year. The school district has a budget of $594,000, and can afford at most 40 mechanical repairs per year. Due to storage space, the school district cannot buy more than 32 buses. How many buses of each type should the school district buy in order to maximize the number of students that the buses can transport? a) Define your variables using full sentences b) Write the objective (Minimize or Maximize) and the objective function. c) Find the constraints. Show all your work.
Consider the following Linear Programming Problem: A school district is buying new buses to transport students in Winnipeg. There are two types of buses available: the Bronco buses and the Neon buses. Each Bronco bus costs 18,000 dollars has a capacity of 25 passengers, and will require 2 mechanical repairs per year. Each Neon bus costs 22,000 dollars has a capacity of 30 passengers, and will require 1 mechanical repair per year. The school district has a budget of $594,000, and can afford at most 40 mechanical repairs per year. Due to storage space, the school district cannot buy more than 32 buses. How many buses of each type should the school district buy in order to maximize the number of students that the buses can transport?
a) Define your variables using full sentences
b) Write the objective (Minimize or Maximize) and the objective function.
c) Find the constraints. Show all your work.
d) Find the feasible set and its corners. Show all your work and also add a sketch describing the lines, shadings, the feasible set and its corners.
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