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  • Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 32 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 32 Maths Textbook Solution.

Answers (1)

Answer:.

The answer of the given questions is that 8 items of type A and 16 of type B should be produced for max profit.

Hint:

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

Given:

A firm makes items A and B and the total number of items it can make in a day is m. It takes one hour to make an item of A and only half an hour to make an item of B. The maximum time available per day is 16 hours.

Solution:      

      

Let the number of items of type A and B produce be x and y respectively.

The LPP is maximize Z=300x+160y

Subject to the constraints.

                  \begin{aligned} &x+y \leq 24 \\ &x \cdot 1+y \cdot \frac{1}{2} \leq 16 \\ &x \geq 0, y \geq 0 \end{aligned}

Draw the lines

                x+y=24                                                           … (i)

                 \begin{aligned} &\\ &x+\frac{1}{2} y=16 \end{aligned}                                                       … (ii)

These meet at P (8, 16)

The feasible region is OCPB

The value of Z = 300x + 160y at 0 is zero

At C(16,0) is 4800

At B(0,24) is 3840

At P(8,16) is 4960

Clearly, value is max at P(8,16)

\Rightarrow 8 items type A and 16 type B should be produced for max. Profit

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