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
7.5k views
in Mathematics by (65.1k points)

A dealer wishes to purchase a number of fans and radios. He has Rs. 5,760 to invest and has a space for at most 20 items. A fan costs him Rs. 360 and a radio Rs. 240. His expectation is that he can sell a fan at a profit of Rs. 22 and a radio at a profit of Rs. 18. Assuming that he can sell and the items he buys, how should he invest his money to get maximum profit ? Translate the problem as LPP and solve is graphically.

1 Answer

+1 vote
by (71.5k points)
selected by
 
Best answer

Let number of fans = x 

and number of radios = y 

max. profit z = 22x + 18y 

according to constraints 

x + y  20 

360x + 240y  5,760 

Now plot the straight lines on the graph and find the corner points of feasible region

∴ Corner points of feasible region are A(16, 0), P(8, 12) and C(0, 20) Corner points Z = 22x + 18y 

A(16, 0) Z = 352 + 0 = 352 

P(8, 12) Z = 176 + 216 = 392 

e(0, 20) Z = 0 + 360 = 360 

∴ Max. profit Z = Rs. 392 at x = 8, y = 12.

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

...