Two vitamins A and B are to be given as health supplements on daily basis to students.
There are two products Alpha & Beta which contain vitamins A and B. One unit of Alpha
contains 2g of A and 1g of B. One unit of Beta contains 1g of A and 2g of B. Daily
requirements for A and B are atleast 10g each. Cost per unit of Alpha is Rs. 20 and of Beta is
Rs. 30. Formulate as LPP to satisfy the requirements at minimum cost
Answers
Answer: Let x and y units of food F
1
and food F
2
were mixed.
Clearly, x≥0 and y≥0
One unit of food F
1
contains 2 units of vitamin A and one unit of food F
2
contains 4 units of vitamin A.
∴ x and y units of food F
1
and food F
2
respectively contains 2x and 4y units of vitamin A.
It is given that the minimum daily requirements for a person of vitamin A is 40 units.
Hence, 2x+4y≥40
One unit of food F
1
contains 3 units of vitamin B and one unit of food F
2
contains 2 units of vitamin B.
∴ x and y units of F
1
and F
2
contains 3x and 2y units of vitamin B.
It is given that the minimum daily requirements for a person of vitamin B is 50 units.
Hence, 3x+2y≥50
One unit of food F
1
and food F
2
cost Rs.50 and 25 respectively.
∴ x and y units of food F
1
and food F
2
costs Rs.50x and Rs.25y respectively.
Let z denote the total cost
Then, z=Rs(50x+25y)
Hence, the required LPP is
Minimize Z=50x+25y
Subject to
2x+4y≥40
3x+2y≥50
x≥0, y≥0
Step-by-step explanation: