Textbook Problem

Biology Repeat Exercise 41 for a salt-content model given by

$S=0.01x^2{y}^2{z}^2$.

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?