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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

Answers (1)

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/- 

 

Posted by

infoexpert26

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