I'm not sure that matrices is the best way to go . . .
Let: .A firm produces three products:
that require processing by three machines: .
The time in hours required for processing one unit of each product
by the three machines is given by the following table:
Macine I is available for 490 hours,
machine II is available for 310 hours,
machine III for 560 hours.
Find how many units of each product should be produced
to make use of all the available time on the machines.
We have three inequalities: .
Solve the system of equations: .
. . and we get: .