Answer to Question #257209 in Operations Research for Haile

Question

The doctor advises a patient visited him that the patient is weak in his health due to shortage of two vitamins, i.e., vitamin A and vitamin D. He advises him to take at least 40 units of vitamin A and 50 units of Vitamin D every day. He also advises that these vitamins are available in two tonics X and Y. Each unit of tonic X consists of two units of vitamin A and three units of vitamin D

Answer 1

This question is incomplete as table is missing:

Let us first add the table

Let the variables $x_{1}$ and $x_{2}$ represent units of tonic $x$ and $y$ respectively.

The total cost of diet consisting of $x_{1}$ units of $x$ and $x_{2}$ units of $y$ is given by, $z=5 x_{1}+3 x_{2}$

Since, the tonics $x$ and $y$ cost Rs 5 per unit and Rs. 3 per unit respectively.

Now, total amount of vitamin A required for the tonic $x$ and $y$ is $2 x_{1}+4 x_{2}$ .

Total amount of vitamin D required for the tonic $x$ and $y$ is $3 x_{1}+2 x_{2}$ .

Again, Since, the minimum daily requirement of vitamin A is 40 units and that of vitamin B is 50 units, therefore must have, $\quad 2 x_{1}+4 x_{2} \geqslant 40$

and $3 x_{1}+2 x_{2} \geqslant 50$

Also since, $x_{1}$ and $x_{2}$ are either positive or zero, we should have $x_{4} \geqslant 0, x_{2} \geqslant 0$

Hence, the formulation of the L.P.P. is

minimize $z=5 x+3 x_{2}$

Subjected to

$2 x+4 x_{2} \geqslant 40 \\ 3 x+2 x_{2} \geqslant 50 \\ x_{1}, x_{2} \geqslant 0$