word problem for an augmented matrix
An auto manufacturer sends cars from two plants. I and II, to dealerships A and B, located in a midwestern city. Plant I has a total of 28 cars to send, and plant II has 8. Dealer A needs 20 cars, and dealer B needs 16. Transportation costs based on the distance of each dealership from each plant are $220 from I to A, $ 300 from I to B, $400 from II to A, $180 from II to B. The manufacturer wants to limit transportation costs to $10,640. How many cars should be sent from each plant to each of the two dealerships?
I am just completely confused on how to begin this problem, and it has be be a matrix. I know it can be solved without one, but I'm pretty sure it's necessary to have the Matrix.
all i have is:
Let x represent plant I
Let y represent plant II
220x + 400 y = ?
300x + 180y = ?
I'm not even sure if this is right... can someone please just explain how to start things, I can do the matrix on my own, I just need a little nudge in the right direction...
thanks so muchh!!