The cruiser bicycle company makes two styles of bicycles the traveler which sells for $200 and the Tourister was sells for $600 each bicycle has the same frame and tires but the assembly and painting time required for the traveler is only one hour while it is three hours for the Tourister they are 300 frames and 360 hours of labor available for production how many bicycles of each model should be produced To maximize revenue
To maximize revenue, we need to determine the optimal number of bicycles to produce for each model. Let's assume we produce x number of Traveler bicycles and y number of Tourister bicycles.
To solve this problem, we need to set up an objective function and constraints.
Objective function: Revenue = Total revenue from Traveler bicycles + Total revenue from Tourister bicycles
= 200x + 600y
Constraints:
1. Frame constraint: Each bicycle requires one frame. So, the total number of frames used should not exceed the available 300 frames.
x + y ≤ 300
2. Labor constraint: The total number of hours required for assembly and painting should not exceed the available 360 hours.
1x + 3y ≤ 360
3. Non-negativity constraint: Both x and y must be non-negative, as we cannot produce negative bicycles.
x ≥ 0
y ≥ 0
Now, we can solve this problem using linear programming techniques.
One way to do this is to graph the constraints on a coordinate plane and identify the feasible region. Then, we can evaluate the objective function at each corner point of the feasible region to find the maximum revenue.
However, since this is a simple problem, we can use a simpler approach called the "corner point method" to obtain the optimal solution.
Step 1: Set up the constraints:
x + y ≤ 300 (Frame constraint)
x + 3y ≤ 360 (Labor constraint)
x ≥ 0, y ≥ 0 (Non-negativity constraint)
Step 2: Determine the corner points of the feasible region:
To find the corner points, we need to solve the system of equations formed by the constraints. Let's find the intersection points:
When x = 0, y = 300 (from the frame constraint)
When y = 0, x = 300 (from the frame constraint)
When x + y = 300, x = 0, y = 300 (frame constraint equation 1)
x + 3y = 360 → y = (360 - x)/3
When x = 0, y = 120 (from the labor constraint)
When y = 0, x = 360 (from the labor constraint)
Solving x + 120 = 360, we get x = 240 and y = 0 (labor constraint equation 1)
The corner points are:
(x, y) = (0, 300), (300, 0), (240, 0)
Step 3: Evaluate the objective function at each corner point:
Revenue = 200x + 600y
When (x, y) = (0, 300): Revenue = 200(0) + 600(300) = $180,000
When (x, y) = (300, 0): Revenue = 200(300) + 600(0) = $60,000
When (x, y) = (240, 0): Revenue = 200(240) + 600(0) = $48,000
Step 4: Compare the revenues and find the optimal solution
The maximum revenue is $180,000 when (x, y) = (0, 300). This means that the cruiser bicycle company should produce 0 Traveler bicycles and 300 Tourister bicycles to maximize revenue.
Therefore, the optimal production plan is to produce 0 Traveler bicycles and 300 Tourister bicycles.