Production   A firm produces three products, A, B, and C, that require processing by three machines, I, II, and III. The time in hours required for processing one unit of each product by the three machines is given by the following table: ABCI312II121III241Machine I is available for 440 hours, machine II for 310 hours, and 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.Is 74, 88, and 60 correct?

Question
Asked Nov 15, 2019
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  Production   A firm produces three products, A, B, and C, that require processing by three machines, I, II, and III. The time in hours required for processing one unit of each product by the three machines is given by the following table:

  A B C
I 3 1 2
II 1 2 1
III 2 4 1


Machine I is available for 440 hours, machine II for 310 hours, and 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.

Is 74, 88, and 60 correct?

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Expert Answer

Step 1

Suppose a firm produces A, B and C that require processing by three machines I, II and III respectively:

 

By the following table:

А В С
I
3 1
2
II 2
1
III 24
1
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А В С I 3 1 2 II 2 1 III 24 1

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Step 2

Given that machine I is available for 440 hours, machine II for 310 hours, and machi...

3A B 2C= 440
(i)
..(ii)
A 2BC 310
2A 4B 2C 560
...(ii)
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3A B 2C= 440 (i) ..(ii) A 2BC 310 2A 4B 2C 560 ...(ii)

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