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Name: Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 13
Uploaded: Tue, 2021-09-07 18:11
Description: Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 13

Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 13

Answers (1)

Answer:

$Max\: Profit \Rightarrow Rs.2150$ when 10 units of item A and 65 units of item B are manufactured.

Hint:

Form Linear Equations and solve graphically.

Given:

A firm manufacturing two types of electric items A and B can make a profit of Rs.20 per unit of A and E 30 per unit of B. Each unit of A requires 3 motors and 4 transformers and each unit of B requires 2 motors and 4 transformers. The total supply of these per month is restricted to 210 motors and 300 transformers Type B is an export model requiring a voltage stabilizer which has a supply restricted to 65 units per month.

Solution:

Let x units of item A and y units of item B are manufactured.

Numbers of items cannot be negative.

Therefore, $x, y \geq 0$

The given information can be tabulated as follows:

Product	Motors	Transformers
$A(x)$	$3$	$4$
$B(y)$	$2$	$4$
Availability	$210$	$300$

Further it is given that type B is an export model, whose supply is restricted to 65 per month.

Therefore, the constraints are

$\begin{aligned} &3 x+2 y \leq 210 \\ &4 x+4 y \leq 300 \\ &y \leq 65 \end{aligned}$

A and B make profit of Rs20 and Rs30 per unit respectively.

Therefore, Profit gained from x units of item A and y units od Item B is Rs. 20 x and 30uy respectively.

$Max \: Profit \Rightarrow z=20x+30y$ which according to question is to be maximized
Thus, mathematical formulation of the given L.P.P is,

Max $z = 10x + 3y$
Subject to constraints,

$\begin{aligned} &3 x+2 y \leq 210 \\ &4 x+4 y \leq 300 \\ &Y \leq 65 \end{aligned}$

$x,y\geq 0$ ; Region represented by $3x+2y\leq \210$ .

The line $3x+2y\leq \210$ meets the axes at A(70,0) , B(0,105) respectively

Region containing the origin represents $3x+2y\leq \210$ as origin satisfies $3x+2y\leq \210$

Region $4x+4y< 300$ : The line $4x+4y< 300$ meets the axes at C75,0, D0,75 respectively.
Region containing the origin represents $4x+4y< 300$ as origin satisfies $4x+4y< 300$