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1. Reference of Example 9 (Diet problem): A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol.
How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?
Answers (1)
Let diet contain x packets of food P and y packets of food Q. Thus, .
The mathematical formulation of the given problem is as follows:
Total cost is Z .
Subject to constraint,
The feasible region determined by constraints is as follows:
The corner points of feasible region are
The value of Z at corner points is as shown :
| corner points |
|
|
| |
150 | MINIMUM |
|
|
285 | maximum |
| 228 |
Hence, Z has a maximum value of 285 at the point.
to maximise the amount of vitamin A in the diet, 40 packets of food P and 15 packets of food Q should be used. The maximum amount of vitamin A is 285 units.
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