Answer:
100 x1 + 130 x2 + 16 x3 = 4758
120 x1 + 180 x2 + 28 x3 = 6504
160 x1 + 190 x2 + 10 x3 = 6720
pt 2
x1 = 15
x2 = 21
x3 = 33
Step-by-step explanation:
From the linear system , number of widgets produced per hour for each machine are x1 = 0.015 units, x2 = 0.021units, and x3 = 0.033units.
" Linear system is defined as the model of the given system which represents set of two or more linear equations."
According to the question,
Linear system formed as per the data given,
[tex]100x_{1} +130x_{2} +16x_{3} = 4.758[/tex] ____(1)
[tex]120x_{1} +180x_{2} +28x_{3}= 6.504[/tex] ____(2)
[tex]160x_{1} +190x_{2} +10x_{3} = 6.720[/tex] ____(3)
Multiply linear equation (1) by 7 and ( 2) by 4 we get,
[tex]700x_{1} +910x_{2} +112x_{3} = 33.306\\480x_{1} +720x_{2} +112x_{3} = 26.016[/tex]
Subtract above linear equation to eliminate [tex]x_{3}[/tex] we get,
[tex]220x_{1} +190x_{2} = 7.29[/tex] ____(4)
Multiply linear equation(2) by 5 and ( 3) by 14 we get,
[tex]600x_{1} +900x_{2} +140x_{3} = 32.52\\2240x_{1} +2660x_{2} +140x_{3} =94.08[/tex]
Subtract above linear equation to eliminate [tex]x_{3}[/tex] we get,
[tex]1640x_{1} +1760x_{2} = 61.56\\\\4( 410x_{1} +440x_{2}) = 61.56[/tex]
[tex]410x_{1} +440x_{2}= 15.39[/tex] ____(5)
Multiply linear equation (4) by 88 and ( 5) by 38 we get,
[tex]19360x_{1} +16720x_{2} = 641.52\\\\15580x_{1} +16720x_{2} = 584.82[/tex]
Subtract above linear equation to eliminate [tex]x_{2}[/tex] we get,
[tex]3780x_{1} =56.7[/tex]
⇒[tex]x_{1} =0.015[/tex]
Substitute the value of [tex]x_{1}[/tex] in (5) we get,
[tex]410(0.015) +440x_{2}= 15.39[/tex]
⇒[tex]x_{2} =0.021[/tex]
Substitute the value of [tex]x_{1} and x_{2}[/tex] in (1) we get,
[tex]100(0.015) +130(0.021) +16x_{3} = 4.758[/tex]
⇒[tex]x_{3} = 0.033[/tex]
Hence, number of widgets produced per hour for each machine are x1 = 0.015 units, x2 = 0.021units, and x3 = 0.033units.
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