<p>I have this math packet for hw and it has loads of problems on systems of equations and matrix. The last few problems have been bothering me. Here it is:</p>
<p>To manufacture an automobile require painting, drying, and polishing. Epsilon Motor Company produces three types of cars: the Delta, the Beta, and the Sigman. Each Delta requires 10 hours of painting, 3 hours of drying, and 2 hours of polishing. A beta requires 16 hours of painting, 5 hours of drying, and 3 hours of polishing, while the Sigma requires 8 hours of painting, 2 hours of drying, and 1 hours of polishing. If the company has 240 hours for painting, 69 hours for drying, and 41 hours for polishing per month, how many of each type of car are produced?</p>
<p>You have to solve it using system of linear equations and then using matrices. Since the matrix part might take time just give me some advice on how to set it up and ill do the math. Thanks.</p>
<p>Your three variables are d, b, s which respectively stand for the number of Deltas, Betas, and Sigmas.</p>
<p>To set up the system of equations, you add up the number of hours task by task. The first equation will be just for the number of hours spent on painting, the second for drying, and the third for polishing.</p>
<p>The first equation: Each model has a different amount of hours spent on painting. Multiply that amount of hours by the number of cars of that model (your variables d, b, or c) to get the total number of hours spent painting all the cars of that model. Then set it equal to the total number of hours the company spent painting.</p>
<p>10d + 16b + 8s = 240</p>
<p>Repeat for the second and third equations and you should get:
10d + 16b + 8s = 240
3d + 5b + 2s = 69
2d + 3b + 1s = 41</p>
<p>To put it into a matrix, create a 3x4 augmented matrix and plug the numbers in.
[10 16 8 | 240]
[3 5 2 | 69 ]
[2 3 1 | 41 ]</p>
<p>Do you need help solving the system of equations?</p>
<p>I would really appreciate it if you could tell me how to do the rest. I tried and im getting random numbers. I hate these kind of problems! Just the matrix part not the equation.</p>
<p>here is what I got from the equation part to make sure.</p>
<p>s = 10
b = 5
d = 8</p>
<p>haha never mind! I got it now. Thanks you saved me.</p>
<p>No prob! Glad I could help. </p>
<p>To tell you the truth, I didn’t solve the problem since I was lazy, but I plugged it into my calculator and got those same answers.</p>