The maximum value of Z=50 x+ 15y subject to the constraints 5 x +y \leq 100, x+y \leq 60, x>0, y \geq 0 is

BPSC 47th Exam Prelims 2005 Solved Paper

Question : 124 of 150

Marks: +1, -0

The maximum value of

Z=50 x+

15y subject to the constraints

5 x

+y ≤ 100, x+y ≤ 60, x>0, y ≥ 0

Solution:

The objective function is

z=50 x+15 y

The constraints are:

5 x+y<100

.....(i)

x+y<60

.....(ii)

x>0

.....(iii)

y>0

...(iv)
The line corresponding to

5 x+y=

100 is

(0,100),

and (20,0)
The line corresponding to

x+y=60

is (0,60) and (60,0)
Now the feasible value of

z=50 x

+15 y

are
At

(0,0) z=50 x+15 y=0+0=0

(20,0) z=50 x+15 y=1000

(10,50) z=50(10)+15(50)=1250

(0,60) z=50(0)+15(60)=900

∴

Maximum value of

z=1250

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