Take Class 12 Tuition from the Best Tutors
Affordable fees 1-1 or Group class Flexible Timings Verified Tutors Search in
Asked by Apoorva Last Modified
Answer 
Vishaka Bhutia
Home Tutor
Let the diet contain x units of food F1 and y units of food F2. Therefore,
x ≥ 0 and y ≥ 0
The given information can be complied in a table as follows.
| Vitamin A (units) | Mineral (units) | Cost per unit (Rs) | |
| Food F1 (x) | 3 | 4 | 4 |
| Food F2 (y) | 6 | 3 | 6 |
| Requirement | 80 | 100 |
The cost of food F1 is Rs 4 per unit and of Food F2 is Rs 6 per unit. Therefore, the constraints are
3x + 6y ≥ 80
4x + 3y ≥ 100
x, y ≥ 0
Total cost of the diet, Z = 4x + 6y
The mathematical formulation of the given problem is
Minimise Z = 4x + 6y … (1)
subject to the constraints,
3x + 6y ≥ 80 … (2)
4x + 3y ≥ 100 … (3)
x, y ≥ 0 … (4)
The feasible region determined by the constraints is as follows.
It can be seen that the feasible region is unbounded.
The corner points of the feasible region are 
.
The corner points are
.
The values of Z at these corner points are as follows.
| Corner point | Z = 4x + 6y | |
|
|
| |
|
| 104 | → Minimum |
|
| 200 |
As the feasible region is unbounded, therefore, 104 may or may not be the minimum value of Z.
For this, we draw a graph of the inequality, 4x + 6y < 104 or 2x + 3y < 52, and check whether the resulting half plane has points in common with the feasible region or not.
It can be seen that the feasible region has no common point with 2x + 3y < 52
Therefore, the minimum cost of the mixture will be Rs 104.
read lessNow ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com
Ask a QuestionRecommended Articles
Meet Radhe Shyam Burman, an MBA Tutor from...
Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...
Read full article >
Meet Sandhya R, a B.Sc tutor from Bangalore
Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...
Read full article >
Meet Swati, a Hindi Tutor from Bangalore
Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...
Read full article >
Meet Urmila, an MBBS tutor from Bangalore
Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition. Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...
Read full article >
Looking for Class 12 Tuition ?
Learn from the Best Tutors on UrbanPro
Are you a Tutor or Training Institute?
Join UrbanPro Today to find students near youThe best tutors for Class 12 Tuition Classes are on UrbanPro
The best Tutors for Class 12 Tuition Classes are on UrbanPro
