A manufacturer produces three models (I, II, and III) of a certain product. He u

Question

A manufacturer produces three models (I, II, and III) of a certain product. He uses two types of raw material (A and B) of which 4000 and 6000 units are available,respectively. The raw material requirements per unit of three models are given below

The labor time for each unit of Model I is twice that of Model II and three times that of Model III. The entire labor force of the factory can produce the equivalent of 600 units of Model I. A market survey indicates that the minimum demand of the three models is 200, 200 and 150 units, respectively. However, the ratios of the number ofunits produced must be equal to 2:5:3. Assume that the profit per unit of Models I, II, and III are 30, 20, and 50 dollars. Formulate the problem as a linear programming model in order to determine the number of units of each product which will maximize profit.

Raw Material Requirements per unit of given models

Explanation / Answer

Let x1 be the number of units of model I

x2 be the number of units of model II

x3 be the number of units of model III

x1 + 1/2x2 + 1/3x3 600 [ Labour time ]

x1 200,x2 200,x3 150[Minimumdemand]

The given ratio is x1:x2:x3 = 2:5:3

x1 / 2 = x2 / 5 = x3 / 3 = k
x1 = 2k; x2 = 5k; x3 = 3k
x2 = 5k k = x2 / 5

Therefore x1=2x2/55x1 =2x2

Similarly 5x3 = 3 x2

Maximize Z= 30x1 + 20x2 + 50x3

Subject to 3x1 + 4x2 + 7x3 4000

2x1 +9x2 +5x3 6000

x1 + 1/2x2 + 1/3x3 600

5x1 =2x2

5x3 = 3 x2

and x1 200,x2 200,x3 150

Now we have to find maximum of this equation,we can do it using online tools we have(it takes a lot of time and space to upload the solution)

Hope this helps,if you have any problem comment in here i will reply

thank you

Raw materials I II III Availability A 3 4 7 4000 B 2 9 5 6000 Profit 30 20 50

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