The Cruiser Bicycle Company makes two styles of bicycles: the Traveler, which sells for $200, and the Tourister, which sells for $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor available for production. How many bicycles of each model should be produced to maximize revenue?
To determine the number of bicycles of each model that should be produced to maximize revenue, we can use a mathematical approach called linear programming.
Let's define our decision variables:
Let x be the number of Traveler bicycles to be produced.
Let y be the number of Tourister bicycles to be produced.
Now, we can establish our objective function and constraints:
Objective function:
We want to maximize the revenue. The revenue is calculated by multiplying the selling price of each bicycle by the number of bicycles sold. Therefore, the objective function is:
Revenue = 200x + 600y
Constraints:
1. Frame constraint: The total number of frames available is 300, and each bicycle requires one frame. Therefore, the constraint is:
x + y ≤ 300
2. Labor constraint: The total available labor hours are 360, and the Traveler requires 1 hour of labor while the Tourister requires 3 hours. Therefore, the constraint is:
x + 3y ≤ 360
3. Non-negativity constraint: The number of bicycles produced cannot be negative. Therefore, the constraints are:
x ≥ 0
y ≥ 0
Now, we have set up the linear programming problem. We need to solve it to find the optimal values of x and y that maximize the revenue.
There are several methods to solve linear programming problems, such as graphical method or simplex method. We will use the simplex method to solve this problem.
After solving the linear programming problem using the simplex method, we can obtain the values of x and y that maximize revenue. These values will represent the number of Traveler and Tourister bicycles to be produced, respectively.