Solve the Problem by Writing and Solving a Suitable System $X, Y$

Multiple Choice

Solve the problem by writing and solving a suitable system of equations.
-A company produces three models of video cassette player, models $X, Y$ , and Z. Each model $X$ machine requires 3.2 hours of electronics work, 2.8 hours of assembly time, and 4.4 hours of quality assurance time. Each model $\mathrm{Y}$ machine requires 5.2 hours of electronics work, 4.4 hours of assembly time, and 5.2 hours of quality assurance time. Each model $\mathrm{Z}$ machine requires 5.2 hours of electronics work, 3.2 hours of assembly time, and 3.8 hours of quality assurance time. There are 440 hours available each week for electronics, 346 hours for assembly, and 453 hours for quality assurance. How many of each model should be produced each week if all available time must be used?

A) 38 model $X$ , 37 model Y, 25 model $Z$
B) 41 model X, 35 model Y, 24 model Z
C) 40 model $X$ , 30 model $Y, 30$ model $Z$
D) 40 model $X$ , 35 model Y, 25 model Z