Question

Set up the system of equations needed to solve the exercise for part (b). Watson Electric has production facilities in Valley Mills, Marlin, and Hillsboro. Each one produces radios, stereos, and TV sets. Their production capacities are as follows:

Valley Mills: 10 radios, 12 stereos, and 5 TV sets per hour
Marlin: 7 radios, 11 stereos, and 6 TV sets per hour
Hillsboro: 2 radios, 3 stereos, and 14 TV sets per hour

Let \(x_1\) = hours at Valley Mills, \(x_2\) = hours at Marlin, \(x_3\) = hours at Hillsboro.

The firm receives an order for 1,055 radios, 1,230 stereos, and 1,470 TV sets. How should each plant be scheduled to produce these amounts?
A) \(10x_1 + 7x_2 + 2x_3 = 1,055\), \(12x_1 + 11x_2 + 3x_3 = 1,230\), \(5x_1 + 6x_2 + 14x_3 = 1,470\)
B) \(10x_1 + 7x_2 + 2x_3 = 1,055\), \(12x_1 + 11x_2 + 3x_3 = 1,230\), \(2x_1 + 3x_2 + 14x_3 = 1,470\)
C) \(5x_1 + 6x_2 + 14x_3 = 1,055\), \(10x_1 + 7x_2 + 2x_3 = 1,230\), \(12x_1 + 11x_2 + 3x_3 = 1,470\)
D) \(2x_1 + 3x_2 + 14x_3 = 1,055\), \(10x_1 + 7x_2 + 2x_3 = 1,230\), \(12x_1 + 11x_2 + 3x_3 = 1,470\)

Answer 1

To determine the production schedules for Watson Electric's three facilities, we set up the system of linear equations based on their hourly production capacities for radios, stereos, and TV sets to fulfill an order.

Step-by-step explanation:

To solve the exercise for part (b), we need a system of equations that represents the production capacities of Watson Electric at the three facilities with regard to their outputs of radios, stereos, and TV sets. Given that x1 represents the hours at Valley Mills, x2 represents the hours at Marlin, and x3 represents the hours at Hillsboro, we can establish the following system of linear equations:

• For radios: 10x1 + 7x2 + 2x3 = 1,055
• For stereos: 12x1 + 11x2 + 3x3 = 1,230
• For TV sets: 5x1 + 6x2 + 14x3 = 1,470

This system reflects the production capacity of each facility per hour and ensures that the total outputs meet the firm's order requirements for radios, stereos, and TV sets.