# A Firm Manufactures Two Products, Each of Which Must Be Processed Through Two Departments, 1 and 2. the Hourly Requirements per Unit for Each Product in Each Department, the Weekly - Mathematics

Sum

A firm manufactures two products, each of which must be processed through two departments, 1 and 2. The hourly requirements per unit for each product in each department, the weekly capacities in each department, selling price per unit, labour cost per unit, and raw material cost per unit are summarized as follows:

 Product A Product B Weekly capacity Department 1 3 2 130 Department 2 4 6 260 Selling price per unit ₹ 25 ₹ 30 Labour cost per unit ₹ 16 ₹ 20 Raw material cost per unit ₹ 4 ₹ 4

The problem is to determine the number of units to produce each product so as to maximize total contribution to profit. Formulate this as a LPP.

#### Solution

The given data can be arranged in the following tabular form:

 Product A Product B Weekly capacity Department 1 3 2 130 Department 2 4 6 260

 Product A Product B Selling price per unit Rs 25 Rs 30 Labour cost per unit Rs 16 Rs 20 Raw material cost per unit Rs 4 Rs 4

Let  $x$  be the number of units of product A.
Let  $y$   be the number of units of product B.
Profit per unit $=$  Selling price per unit  $-$  Labour cost per unit  $-$  Raw material cost per unit
Profit on one unit of product A $= 25 - 16 - 4 =$  Rs $5$ Profit on one unit of product B $= 30 - 20 - 4 =$    Rs 6 Totat profit

z= 5x + 6y

According to the question,

$3x + 2y \leq 130$

$4x + 6y \leq 260$

$x \geq 0, y \geq 0$

Concept: Mathematical Formulation of Linear Programming Problem
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#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 30 Linear programming
Exercise 30.1 | Q 16 | Page 17