Question 1127020: Tv Pro Inc . produces three models of tv sets: economy , deluxe, and super. Each economy Tv set requires 2 hrs of electronics work, 2 hr of assembly time,and 1 hour of finishing time. Each deluxe Tv set requires 1 hour of electronics work , 3 hours of assembly time, and 1 hour of finishing time. Each super TV set requires 3 hours of electronics work, 2 hours of assembly time, and 2 hours of finishing time. There are 158 hours of labor available for electronics work, 168 hours for assembly, and 104 hours available for finishing each week. How many of each model should be produced each week if all time for labor is to be used?
Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website! .
Tv Pro Inc . produces three models of tv sets: economy , deluxe, and super.
Each economy Tv set requires 2 hrs of electronics work, 2 hr of assembly time,and 1 hour of finishing time.
Each deluxe Tv set requires 1 hour of electronics work , 3 hours of assembly time, and 1 hour of finishing time.
Each super TV set requires 3 hours of electronics work, 2 hours of assembly time, and 2 hours of finishing time.
There are 158 hours of labor available for electronics work, 168 hours for assembly, and 104 hours available for finishing each week.
How many of each model should be produced each week if all time for labor is to be used?
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See how I edited the condition to extract each the condition sentence in one separate line.
It helps A LOT in solving the problem (!)
Let E = #Economy TV; D = #deluxe TV; S = #super TV.
Then the Math model consists of these 3 equations in 3 unknowns:
2E + 1D + 3S = 158 (1) (hours of electronic work)
2E + 3D + 2S = 168 (2) (hours of assembly work)
1E + 1D + 2S = 104 (3) (hours of finishing work)
At this point the setup is just done.
Now, the system can be solved by different methods: Elimination, Substitution, Cramer's rule.
In my life I solved similar systems many times, so I do not need to exercise more.
Also, I know that the manual procedure is boring.
Therefore, instead solving it manually, I will use an online solver - the free of charge Gauss elimination solver from the site www.reshish.com.
https://matrix.reshish.com/gaussSolution.php
The solution from the solver is E = 24, D = 20, S = 30.
It is your ANSWER.
Thus the problem is just solved.
The fact that you found the solution in integer non-negative numbers means that this solution provides that all time for labor is used.
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By the way, the solvers at this site have the mode explaining the solution steps in a very detailed manner - as a dedicated tutor does !
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