Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
124 views
in Linear Programming by (91.4k points)
closed by
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?

1 Answer

0 votes
by (91.3k points)
selected by
 
Best answer
Let the manufacturer produces `x` packets of nuts and `y` packets of bolts, then
image
`:.` Maximise `Z=17.5x+7y`……………….1
and constraints `x+3yle12`………………………2
`3x+yle12`………………….3
`xge0,yge0`………………...4
image
First draw the graph of the line `x+3y=12`.
image
Put `(0,0)` in the inequation `x+3yge12` ,
`0+3xx0le10implies0le12` (True)
Therefore half plane contains the origin. Since `x,yge0`. So the feasible region is in first quadrant,
Now draw the graph of the line `3x+y=12`
image
Put `(0,0)` in the inequation `3x+yle12`,
`3xx0+0le12gt0le12` (True)
Therefore, the half plane contains the origin.
From the equations `x+3y=12` and `3x+y=12`, the point of intersection is `B(3,3)`.
`:.` The feasible region is OABCO whose vertices are `O(0,0),A(4,0),B(3,3)` and `C(0,4)`. Now, we find the value of `Z` at these points,
image
The value of `Z` is maximum Rs. 73.50 at point `(3,3)`. Therefore, the maximum profit of Rs. 73.50 can be obtained when 3 packets of nuts and 3 packets of bolts are produced per day.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...