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Need solution for RD Sharma Maths Class 12 Chapter 29 Linear Programmig Excercise 29.4 Question 16
Answers (1)
Answer:
Codeine Quantity = 24(approx.) and least quantity of pill A=5.86 and B =0.27
Hint:
Form Linear Equation and solve graphically.
Given:
A firm manufactures headache pills in two sizes A and B. Size A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grain of codeine, Size B contains 1 grain of aspirin and 18 grains of bicarbonate and 66 grains od codeine. It has been found by users that it requires at least 12 grains of aspirin. 7.4 grains of bicarbonate and 24 grains of codeine for providing immediate effect.
Solution:
The above LPP can be presented in a table below,
|
|
|
|
|
|
|
|
|
|
|
Aspirin |
|
|
|
|
Bicarbonate |
|
|
|
|
Codeine |
|
|
|
|
Relief |
|
|
minimize |
Hence mathematical formulation of the given L.P.P is,
Max z = x + y
Subject to constraints,
[Since production cannot be less than 0]
The corner points are B(0,12), P(5.86,0.27),?(24,0).
The value of z at these corner points are as follows.
|
Corner Points |
|
|
(0,12) |
12 |
|
(24,0) |
24 |
|
(5.86,0.27) |
6.13 |
The maximum value of z is 6.13 but the region is unbounded so check whether
Clearly it can be seen that it does not has any common region
So,
This is the least quantity of Pill A and B
Codeine quantity
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