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.

1 answer

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.