A microbiologist must prepare a culture medium in which to grow a certain type of bacteria. The percent of salt contained in this medium is given by

S = 12 x y z

where

x , y,

and

z

are the 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?
A)

\begin{array} { l } x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\y = \sqrt [ 3 ] { 0.065 } \approx 0.201 L \\z = \sqrt [ 3 ] { 0.065 } \approx 0.134 L\end{array}

\begin{array} { l } x = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\z = \sqrt [ 3 ] { 0.015 } \approx 0.2466 L\end{array}

\begin{array} { l } x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\z = \sqrt [ 3 ] { 0.055 } \approx 0.380 L\end{array}

\begin{array} { l } x = \sqrt [ 3 ] { 0.025 } \approx 0.292 L \\y = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\z = \sqrt [ 3 ] { 0.115 } \approx 0.486 L\end{array}

\begin{array} { l } x = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\z = \sqrt [ 3 ] { 0.265 } \approx 0.642 L\end{array}

The Sum of the Length (Denote by Z) and the Girth

Multiple Choice