Let's denote the number of meters of suiting, shirting, and woolens produced as x1, x2, and x3 respectively.
The objective is to maximize the profit, which can be formulated as:
Maximize Z = 2x1 + 4x2 + 3x3
Subject to the following constraints:
3x1 + 4x2 + 3x3 <= 60 (Weaving constraint)
2x1 + x2 + 3x3 <= 40 (Processing constraint)
x1 + 3x2 + x3 <= 80 (Packing constraint)
x1, x2, x3 >= 0
Now, we can solve this linear programming problem using a method like the Simplex method or graphical method to find the optimal solution.
A company has three operational departments namely weaving, processing and packing with capacity to produce three different types of clothes namely suiting’s, shirting’s and woolens yielding a profit of rupees 2 ,4and 3 per meter respectively.1 meter of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing. Similarly 1 meter of shirting requires 4 minutes in weaving ,1 minute in processing and 3 minutes in packing.1 meter of woolen requires 3 minutes in each department .In a week total run time of each department is 60,40 and 80 hours for weaving, processing and packing respectively. Formulate this as LPP and find the solution.
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