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  • Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 4

Explain solution RD Sharma class 12 Chapter 29 Linear Programming exercise 29.4 question 4

Answers (1)

Answer:

The factory produces 30 and 20 packages of screw A and screw B to get the maximum profit.

Hint:

let factory manufacture x screws of type A and y screw of type B.

Given:

The information can be competed in table follow

 

Screw A

Screw B

Availability

Automatic machine (min)

4

6

4\times 60 = 120

Hand operated machine (min)

6

3

4\times 60 = 120

 

Solution:

Let the factory manufacture x screws of type A and y screws of type B on each day.

x\geq 0, y\geq 0

The profit on a package of screws A is Rs 7 and on the package of screws B is Rs 10.

The constraints are

4x+6y\leq 240

6x+3y\leq 240

Total profit z=7x+10y

The required LPP

Max  z=0.7x+y

Subject to constraints

4x+6y\leq 240    ....(i)

6x+3y\leq 24      ....(ii)

x, y\geq 0

The feasible region determined by the system of constraints is

Points (30,20) solution obtain by solving (i) and (ii). The corner points A(40,0), B(30,20) and C(0,40).

Points

z=0.7x+y

A(40,0)

28

B\left ( 30,20 \right )

41

C\left (0,40 \right )

40

The maximum value of z=41 at (30,20).

Thus, the factory should produce 30 packages of screw A and 20 packages of screw B to get the maximum profit of Rs41.

Posted by

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