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  • Provide solution for RD sharma maths class 12 chapter 29 Linear Programming exercise Fill in the blanks question 8

Provide solution for RD sharma maths class 12 chapter 29 Linear Programming exercise Fill in the blanks question 8

Answers (1)

Maximum value=140

Hint:

Form the constraints coordinates (x,y)

Given:

The maximum value of z=3x+4y subject to constraints x+y\leq 40,x+2y\leq 60,x\leq 0,y\leq 0 is _____

Solution:

From the constraints

x+y\leq 40

  x+y= 40         … (i)

x  

0

40

y

40

0

x+2y\leq 60

x+2y= 60       …..ii

x  

0

60

y

30

0

Here,

\begin{aligned} &x+y=40 \\ &x=40-y \end{aligned}

Put x=40-y in (ii)

\begin{aligned} &40-y+2 y=60 \\ &40+y=60 \\ &y=20 \\ &\therefore x=20 \end{aligned}

Now,

\begin{aligned} &z=3 x+y \\ &A(20,20)=3(20)+4(20)=140 \\ &B(40,0)=3(40)+0=120 \\ &C(0,0)=0 \\ &D(0,30)=4(30)=120 \end{aligned}

Therefore, maximum value =140 at (20,20)

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Info Expert 29

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