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Get Answers to all your Questions
3. A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg of food are given below:
| Food | Vitamin A | Vitamin B | Vitamin C |
| X | 1 | 2 | 3 |
| Y | 2 | 2 | 1 |
One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet.
Answers (1)
Let mixture contain x kg of food X and y kg of food Y.
The mathematical formulation of the given problem is as follows:
Minimize :
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of the feasible region are
The value of Z at corner points is as shown :
| corner points |
|
|
| |
160 | |
|
|
112 | minimum |
| |
116 | |
| |
160 |
The feasible region is unbounded, therefore 112 may or may not be maximum value of Z.
For this, we draw and check whether the resulting half-plane has a point in common with the feasible region or not.
We can see feasible region has no common point .
Hence, Z has a minimum value of 112 at point
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