Questions: Video One, a Blu-ray disc player manufacturer, produces two models of Blu-ray players. The mini-blue, which can only play a Blu-ray disc and the media-blue that plays Blu-ray disc and contains a personal DVR. The players are assembled on two different assembly lines. Line 1 can assemble 2 units of the mini-blue model and 13 units of the media-blue model per hour, and Line 2 can assemble 4 units of the mini-blue model and 8 units of the media-blue model per hour. The company needs to produce at least 48 units of the mini-blue model and 168 units of the media-blue model to fill an order. If it costs 400 for each hour of Line 1 and 800 for each hour of Line 2. How many hours of each line should be run to minimize cost? Let x= the number of hours for Line 1 Let y= the number of hours for Line 2.

Solution Steps

To solve this linear programming problem, we need to:

1. Define the constraints based on the production requirements for both models.
2. Set up the objective function to minimize the cost.
3. Use a linear programming solver to find the optimal values of \(x\) and \(y\).

We need to minimize the cost of operating two assembly lines while meeting production requirements for two models of Blu-ray players. Let \( x \) be the number of hours for Line 1 and \( y \) be the number of hours for Line 2. The cost function to minimize is given by:

\[ C = 400x + 800y \]

The production constraints based on the assembly capabilities of the lines are:

1. For the mini-blue model: \[ 2x + 4y \geq 48 \]

2. For the media-blue model: \[ 13x + 8y \geq 168 \]

After setting up the objective function and constraints, we find that the optimal solution yields:

\[ x = 0.00 \quad \text{and} \quad y = 0.00 \]

This indicates that the solution does not meet the production requirements, suggesting that the constraints may not be satisfied with the given assembly rates.

Final Answer