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  • Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 26

Provide Solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 26

Answers (1)

Answer:

4 pedestal lamps and 4 wooden shades

Hint:

By using the mathematical formulation of the given Linear programming is Max Z= ax+by

Given:

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of grinding/ cutting machine and a sprayer. It takes 2 hours on the grinding/ cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp while it takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, line sprayer is available for at most 20 hours and the grinding/ cutting machine for at most 12 hours. The profit from the sale of a lamp is Rs.5.00 and a shade is Rs.3.00. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit?

Solution:

Let the cottage industry manufactures x pedestal lamps & y wooden shades

Therefore,

                x \geq 0, y \geq 0

The given information is as follow:

 

Lamps

Shades

Availability

Grinding machine

2

1

12

Sprayer

3

2

20

 

The profit on a lamp is Rs.5 and on the shades is Rs.3

Max Z = 5x + 3y                                                                 … (i)

Subject to constraints:

                \begin{aligned} &2 x+y \leq 12 \\ & \end{aligned}                                                        … (ii)

                3 x+2 y \leq 20 \\                                                     … (iii)

                x, y \geq 0                                                                … (iv)

The feasible region is as follows:

Corner points z= 5x+3y
\left ( 6,0 \right ) 30
\left ( 4,4 \right ) \\32
\left ( 0,10 \right ) \\30

Maximum value of z= 32 at (4,4)

 

 

Posted by

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