A firm produces three products A,B & C. Its uses two types of raw materials I & II of which 5000 and 7500 units respectively are available. The raw material requirements per unit of product are given below:
Raw MaterialRequirement per unit of product
A; B; C
I: 3; 4; 5
II: 5; 3; 5

The labour time for each unit of product A is twice that of product B and three times that of product C. The entire labour force of the firm can produce the equivalent of 3000 units. The (marks) minimum demand of the three products is 600, 650 and 500 units respectively. Also, the ratios of the number of units must be equal to 2:3:4. Assuming the profits per unit of A,B & C as Rs. 50, 50 and 80 respectively.
Formulate the problem as linear programming model in order to determine the number of units of each product which will maximize the profit.

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Dear Clough
Thanks for the information.

Clough, I would like to tell you that I have not posted this question to get any answer to my homework problem, rather I was just going through one book and found this question. The problem was that I was not satisfied with the equations made in that book.
Problem is with the equation for the line written in bold.

As per solution in the book equation for above line becomes x1 + 1/2 x2 +1/3 x3 ≤ 3000 i.e. 6x1 + 3x2 + 2x3 ≤ 18000 but as per my calculation because ratio between labour time becomes 6:3:2 and it is given that total 3000 units can be produced by entire labour, I believe equation shall be 6x1 + 3x2 + 2x3 ≤ 3000. Please help me in correcting my problem.

I believe now you will put your efforts to help me.
Regards
Parag