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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 10

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 10

Answers (1)

Answer:

Maximum profit Rs22.2.

Hint:

Let daily production of chairs and table be x and y.

Given:

Profit on each chair and table are Rs3 and Rs5.

Solution:

Let 2 be total profit on table and chair 

Max  z=3x+5y  [when x and y are daily production on table and chair]

Since each chair and table require 2hrs and 4hrs on a machine A but maximum time available on machine A be 16 hrs.

\begin{aligned} &2 x+4 y \leq 16 \\ & \end{aligned}

x+2 y \leq 8

Since each chair and table require 6hrs and 2hrs on machine B, but maximum time available on machine B be 30 hrs.

\begin{aligned} &6 x+2 y \leq 30 \\ & \end{aligned}

3 x+y \leq 15

The required LPP is

Max z=3x+5y

Subject to constraints

\begin{aligned} &x+2 y \leq 8 \ldots(i) \\ & \end{aligned}

3 x+y \leq 15 \ldots(i i)

The feasible region obtains by the system of constraints

 

P(\frac{22}{5},\frac{9}{5})   obtain by solving equation (i) and (ii).

OA_{2}PB_{1} are the shaded region

Corner Points

Value of z=2x+1.5y

O\left ( 0,0\right )

0

A_{2}(5,0)

15

P(\frac{22}{5},\frac{9}{5})

22.2

B\left ( 10,4 \right )

20

Hence maximum profit  =Rs 22.2 \left ( \frac{22}{5} ,\frac{9}{5}\right )

 

Posted by

infoexpert27

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