Question #257209
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
1
Expert's answer
2021-11-02T15:58:49-0400

This question is incomplete as table is missing:

Let us first add the table



Let the variables x1x_{1} and x2x_{2} represent units of tonic xx and yy respectively.

The total cost of diet consisting of x1x_{1} units of xx and x2x_{2} units of yy is given by, z=5x1+3x2z=5 x_{1}+3 x_{2}

Since, the tonics xx and yy cost Rs 5 per unit and Rs. 3 per unit respectively.

Now, total amount of vitamin A required for the tonic xx and yy is 2x1+4x22 x_{1}+4 x_{2} .

Total amount of vitamin D required for the tonic xx and yy is 3x1+2x23 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, 2x1+4x240\quad 2 x_{1}+4 x_{2} \geqslant 40

and 3x1+2x2503 x_{1}+2 x_{2} \geqslant 50

Also since, x1x_{1} and x2x_{2} are either positive or zero, we should have x40,x20x_{4} \geqslant 0, x_{2} \geqslant 0

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

minimize z=5x+3x2z=5 x+3 x_{2}

Subjected to

2x+4x2403x+2x250x1,x202 x+4 x_{2} \geqslant 40 \\ 3 x+2 x_{2} \geqslant 50 \\ x_{1}, x_{2} \geqslant 0


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS