Question

In order to supplement daily diet, a person wishes to take some X and some wishes Y tablets. The contents of iron, calcium and vitamins in X and Y (in milligrams per tablet) are given as below:

Tablets	Iron	Calcium	Vitamin
X	6	3	2
Y	2	3	4

The person needs at least 18 milligrams of iron, 21 milligrams of calcium and 16 milligram of vitamins. The price of each tablet of X and Y is Rs 2 and Re 1 respectively. How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost?

Answer 1

From the figure, we can see the feasible region is unbounded region, with comer points as A(8, 0), B(6,1), C(1, 6), and D(0, 9)

Thus, the minimum value of Z is ‘8’ occurring at B( 1, 6). Since the feasible region is unbounded, ‘8’ may not be the minimum value of Z. To decide this, we plot the inequality 2x+y < 8 and check whether the resulting open half has points common with feasible region or not If it has common point, then 8 will not be the minimum value of Z, otherwise 8 will be the minimum value of Z. Thus, from the graph it is clear that, it has no common point. Therefore, Z= 2x + y has 8 as minimum value subject to the given constrains. Hence, the person should take 1 unit of X tablet and 6 units of Y tablets to satisfy the given requirements and at the minimum cost of Rs 8.