Continental Motors manufactures taxis and airport limousines at its two plants. Plant A produces 75 taxis and 6 limousines daily, while plant B produces 50 taxis and 2 limousines daily. To fulfill its contractual obligations for November, the company must manufacture 3,124 taxis and 206 limousines. How many days should the company operate each plant if it wants to exactly meet its contracts?
Is the equation: 75t + 6L = 3,125
50t + 2L = 206
I have to find the equation before I can start with my augmented matrix. Can anyone help?
Days operating plant A = x
Days operating plant B = y
75 x + 50 y = 3124
6 x + 2 y = 206
Thank you so much!
75 50 3124
6 2 206
1 2/3 41.65
1 1/3 34.33 subtract for new row 2
1 2/3 41.65
0 1/3 7.32 double row 2 and subtract for new row one
1 2/3 41.65
0 2/3 14.64
1 0 27.0
0 2/3 14.64 multiply row 2 by 3/2
1 0 27.0
0 1 22.0
I don't particularly like to work with fractions so I went about it this way and came up with the same answer:
75 50 3125 6R1-75R2 into R2
6 2 206
75 50 3125
0 150 3300 R2 divided by 150 into R2
75 50 3125
0 1 1100 R1 - 50R2 into R1
75 0 2025
0 1 22 R1 - 50R2 into R1
75 0 2025
0 1 22 R1 divided by 75 into R1
1 0 27
0 1 22
Thanks again!
Yes, you've correctly identified the equations to represent the production constraints of Continental Motors. However, there seems to be a small mistake in the first equation. The equation should be:
75t + 6L = 3124 (representing the production of taxis)
50t + 2L = 206 (representing the production of limousines)
To solve this system of equations using an augmented matrix, we need to write the matrix equation in the form [A | B], where A is the matrix of coefficients, and B is the matrix of constants. The augmented matrix would be:
[ 75 6 | 3124 ]
[ 50 2 | 206 ]
Now, you can proceed to solve this system of equations using various methods like Gaussian elimination, matrix inverses, or row operations.