Superway Inc. produces four models of computers. Each Model X computer requires

Question

Superway Inc. produces four models of computers. Each Model X computer requires 3.2 labor-hours in the electronics division, 1.5 labor-hours in the manufacturing divisions and 2 labor-hours in the assembly division. Each Model Y computer requires 2.2 labor-hours in the electronics division, 1.2 labor-hours in the manufacturing division and 1 labor -hour in the assembly division . Each Model Z computer requires 2.2 labor-hours in the electronic division, 1.6 labor-hours in the manufacturing division and 1 labor-hour in the assembly division. Each Model Q computer requires 2.6 labor-hour in the electronics division, 2 labor-hours in the manufacturing division and 2 labor-hours in the assembly division. In additional 30 minutes of labor is required for testing each computer produced. Every week Superway has available 1000 labor-hours in the electronics division, 592 labor-hours in the manufacturing assembly division,520 labor-hours in the assebly division, and 212 labor-hours in the testing division. How many of each model should be produced per week so that all available labor-hours are used?

Definition of Variables:

System of Equations:

Answers in Words:

Explanation / Answer

Suppose X type computers produced are a in numbers

Suppose Y type computers produced are b in numbers

Suppose Z type computers produced are c in numbers

Suppose Q type computers produced are d in numbers

..........

Therefore

Total work hours in Electronics division = 3.2a + 2.2b + 2.2c + 2.6d

Total work hours in Manufacturing division = 1.5a + 1.2b + 1.6c + d

Total work hours in Assembly = 2a+b+c+2d

extra 30 minutes of labour for each type = 0.5 labour hours X total produced = (0.5)X( a+b+c+d)

---------------

Given 1000 labour hours in electronics division

therefore equation (1)

3.2a + 2.2b + 2.2c + 2.6d = 1000 --------------- (1)

Given 592 labour hours in manufacturing division

therefore eqn 2

1.5a + 1.2b + 1.6c + d = 592 ....................... (2)

Given 520 labour hours in assembly division

therefore eqn 3

2a+b+c+2d = 520 ........................(3)

Given 212 labour hours in assembly division

therefore eqn 4

0.5a +0.5b +0.5c +0.5d = 212------------------(4)

Solve all equations , since there are 4 variables , 4 equations

We get on solving =

So Type X would be

3.2a+1.5b+2c = Putting a ,b,c values = 743.6 or 743 computers since always less will be produced

So Type Y would be

2.2a+1.2b+1c = Putting a ,b,c values = 460 computers

So Type Z would be

2.2a+1.6b+1c = Putting a ,b,c values = 512.8 or 512 computers

So Type Q would be

2.6a+2b+2c = Putting a ,b,c values = 780.8 or 780 computers

Type of Model /Type of Labour Hours Electronics Manufacturing Assembly X 3.2 1.5 2 Y 2.2 1.2 1 Z 2.2 1.6 1 Q 2.6 2 2

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