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How Many Packets of Each Food Should Be Used to Maximize the Amount of Vitamin a in the Diet? What is the Maximum Amount of Vitamin a in the Diet? - Mathematics

Refer to Example 9. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

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Solution

Let the diet contain and y packets of foods P and Q respectively. Therefore,

x ≥ 0 and y ≥ 0

The mathematical formulation of the given problem is as follows.

Maximize = 6+ 3y … (1)

subject to the constraints,

The feasible region determined by the system of constraints is as follows.

The corner points of the feasible region are A (15, 20), B (40, 15), and C (2, 72).

The values of at these corner points are as follows.

Corner point z = 6x + 3y  
A(15, 20) 150  
B(40, 15) 285 → Maximum
C(2, 72) 228  

Thus, the maximum value of z is 285 at (40, 15).

Therefore, to maximize 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 in the diet is 285 units.

 

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APPEARS IN

NCERT Class 12 Maths
Chapter 12 Linear Programming
Q 1 | Page 525
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