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  • Need solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.1 question 11

Need solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.1 question 11

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Answer:   Min z=150 x+200 y

                  Sub to

\begin{aligned} &2 x+5 y \geq 30 \\ &x+y \geq 8 \\ &x, y \geq 0 \end{aligned}

Min. cost is 1350                                                                                                     

Hint:         Let x and y  in given condition.

Given:      The labour cost to produce at least 60 shirts and 32 pants.

Solution:   Let A works for x days, and

                           B works for y days.

Objective function:

                 Min z=150 x+200 y

                  Sub to

\left.\begin{array}{l} 6 x+10 y \geq 60 \\ 3 x+5 y \geq 30 \end{array}\right\}.....(1)

\left.\begin{array}{l} 4 x+4 y \geq 32 \\ x+y \geq 8 \end{array}\right\} \cdots \cdots(2)

The co-equation of (1) and (2) is

\begin{aligned} &x+y=8 \\ &3 x+5 y=30 \end{aligned}

Solve (2) and (3) we get, c(5,3)

Hence,ACB  are feasible region

\begin{array}{|c|c|} \hline \text { Corner } & \text { Value of } Z=150 x+200 y \\ \hline 0,8 & 0 \\ \hline 10,0 & 1500 \\ \hline 5,3 & 1350 \\ \hline \end{array}

change A(10,0) => 1500, B(5,3)=> 1350 ,C(0,8)=> 1600

Thus,  stitching  5  shirts  and  3  pants  minimizes  labour  cost  to  Rs  1350/- 

 

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