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  • Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 20 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 20 Maths Textbook Solution.

Answers (1)

Answer:

Max Profit = Rs.165 when 3 units of each type of trunk is manufactured.

Hint:

Form Linear Equation and solve graphically.

Given:

A manufacturer produces two types of steel trunks. He has two machines A and B. For completing the first type of the trunk requires 3 hours on machine A and 3 hours on Machine B. whereas the second type of the trunk requires 3 hours on Machine A and 2 hours on Machine B. Machine A and B can work at most for 18 hours and 15 hours per day respectively. He earns a profit of Rs.30 and Rs.25 per tank of the first type and the second type respectively.

Solution:

Let x be trunks of first type and y trunks of second type were manufactured. Number of trunks cannot be negative.

Therefore,  x, y \geq 0

According to the question, the given information can be tabulated as

 

 

Machine A (hours)

Machine B (hours)

First type (x)

3

3

Second type (y)

3

2

Availability

18

15

 

Therefore, the constraints are,

\begin{aligned} &3 x+3 y \leq 18 \\ &3 x+2 y \leq 15 \end{aligned}

He earns a profit of Rs.30 and Rs.25 per trunk of the first type and second type respectively. Therefore, profit gained by him from x trunks of first type and y trunks of second type is Rs.30x and Rs.25y respectively.

Total Profit:  Z=30x+25y

Subject to

\begin{aligned} &3 x+3 y \leq 18 \\ &3 x+2 y \leq 15 \\ &x, y \geq 0 \end{aligned}

Region  3 x+3 y \leq 18  : line  3x+3y=18   meets areas at A(6,0), B(0,6) respectively. Region containing origin represents the solution of the in equation 3 x+3 y \leq 18   as (0,0) satisfies
Region  3 x+2 y \leq 15:  line   3 x+2 y=15  meets areas at  C(5,0), \mathrm{D}\left(0, \frac{15}{2}\right)   respectively. Region containing origin represents the solution of the in equation  3 x+2 y \leq 15  as (0,0) satisfies  3 x+2 y \leq 15

Region x, y \geq 0  : it represents first quadrant.

The corner points are O(0,0), B(0,6), E(3,3) and C(5,0)’

The value of Z at the corner points are as follows.

Corner Points

z=30x+25y

O

0

B

150

E

165

C

150

The maximum value of Z is 165 which is attained at E(3,3)

Thus, the maximum profit is of Rs.165 obtained when 3 units of each type of trunk is manufactured.

Posted by

infoexpert27

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