Nutrition A biologist is performing an experiment on the effects of various combinations of vitamins. She wishes to feed each of her laboratory rabbits a diet that contains exactly 9 mg of niacin, 14 mg of thiamin, and 32 mg of riboflavin. She has available three different types of commercial rabbit pellets; their vitamin content (per ounce) is given in the table. How many ounces of each type of food should each rabbit be given daily to satisfy the experiment requirements?
The requirements of each Type of food for each rabbit.
Answer to Problem 41E
It is impossible to feed the rabbits a diet which satisfies experiment requirements.
Explanation of Solution
Given:
The diet contains
Type-A food vitamins content are
Type-B food vitamins content are
Type-C food vitamins content are
Calculation:
Let the quantity (in ounces) of food Type-A is x,
The quantity (in ounces) of food Type-B is y and,
The quantity (in ounces) of food Type-C is z.
To get the quantity of each Type of food required for each rabbit, convert all the facts into equations
Type-A, Type-B and Type-C foods contain
Type-A, Type-B and Type-C foods contain
Type-A, Type-B and Type-C foods contain
Thus, the system of equation is
To get the complete solution of system transform it into triangular system.
To get triangular system eliminate term x from equation (2) and terms x and y from equation (3).
Multiply equation (1) by
And multiply equation (2) by 2,
Add equation (5) and (4) to eliminate terms x from equation (2) as the coefficients x-terms in both equations are negative of each other,
The equation (6) is new equation (2) for triangular system.
Multiply equation (1) by
And add equation (3) and (7) to eliminate terms x from equation (3) as the coefficients of both equations are negative of each other,
Subtract equations (6) from equation (3) to eliminate terms y from equation (3),
Thus, the triangular system is,
In this triangular system third equation
Third equation is false hence, the system has no solution.
Therefore, it is impossible to feed the rabbits a diet which satisfies experiment requirements.
Chapter 10 Solutions
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