Question

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.
please amswer quickly.this question is from OT​

Answer 1

Answer:

A company has three operational departments (Weaving, processing andpackaging) with capacity to produce three different types of clothes namely suitings,shirtings and woolens yielding the profit k£.2, k£.4 and k£.3 per meter respectively.One-meter suiting requires 3 minutes in weaving, 2 minutes in processing and 1minute in packing. Similarly one meter of shirting requires 4 minutes in weaving, 1minute in processing and 3 minutes in packing while one meter woolen requires 3minutes in each department. In a week, the total run time of each department is 60, 40and 80 hours for weaving, processing and packing departments respectively.Formulate the Linear programming problem to find the product mix to maximize theprofit

Answer 2

Linear programming problems

Given:

All the information given is attached in the image in tabular form.

To find:

LPP formulation of these conditions and solution of it.

Explanation:

The key factor is to determine the weekly rate of production for the three types of  clothes.

Let x, y, z be the weekly production of Suiting's, Shirting's, and Woolen's

respectively.

We know that 1 hour has 60 minutes, so, given information is in hours, we will change it into minutes.

$x\geq 0,\\ y\geq0, \\z\geq0$

The constraints:

$3x + 4y + 3z \leq3600\\\\2x + y + 3z \leq 2400\\\\x + 3y+ 3z\leq4800$

The objective is to maximize the total profit from sales

The total profit therefore is denoted by, $Z= 2x+4y+3z$.

The mathematical formulation of LPP is

Maximize, $Z= 2x+4y+3z$.

Subject to the constraints:

$3x + 4y + 3z \leq3600\\\\2x + y + 3z \leq 2400\\\\x + 3y+ 3z\leq4800$

And

$x\geq 0,\\ y\geq0, \\z\geq0$