Biology Repeat Exercise 41 for a salt-content model given by
Biology A microbiologist must prepare a culture medium in which to grow a certain type of bacteria. The proportion of salt in this medium is given by
S = 12xyz where x, y, and z are the amounts (in liters) of the three nutrient solutions to be mixed in the medium. For the bacteria to grow, the medium must be 13% salt. Nutrient solutions x, y, and z cost $1, $2, and $3 per liter, respectively. How much of each nutrient solution should be used to minimize the cost of the culture medium?
To calculate: The quantity of each nutrient that solution should be used to minimize the cost of medium solution
Given information:
The proportion of salt in the medium is given by;
The medium must have 13% salt and the nutrient solution x, y and z cost is $1, $2, & $3 per litre respectively.
Formula used:
The standard equation is;
If
Where
Calculation:
Consider the given equation,
Now, consider the given function where
Now, the constraint is
Consider the standard equation;
Now, differentiate the above equation with respect to x, y, z and
Equating the above each equation to zero to get the critical points as;
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