Take Class 12 Tuition from the Best Tutors
Search in
A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used tomaximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A?
Let the diet contain x and y packets of foods P and Q respectively. Therefore,
x ≥ 0 and y ≥ 0
The mathematical formulation of the given problem is as follows.
Maximize z = 6x + 3y … (1)
subject to the constraints,
The feasible region determined by the system of constraints is as follows.
The corner points of the feasible region are A (15, 20), B (40, 15), and C (2, 72).
The values of z at these corner points are as follows.
Corner point | z = 6x + 3y | |
A(15, 20) | 150 | |
B(40, 15) | 285 | → Maximum |
C(2, 72) | 228 |
Thus, the maximum value of z is 285 at (40, 15).
Therefore, to maximize the amount of vitamin A in the diet, 40 packets of food P and 15 packets of food Q should be used. The maximum amount of vitamin A in the diet is 285 units.
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 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...
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...
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...
Meet Raghunandan.G.H, a B. Tech Tutor from...
Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...
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