A Microbiologist Must Prepare a Culture Medium in Which to Grow

question 75

Multiple Choice

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) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\
• y = \sqrt [ 3 ] { 0.065 } \approx 0.201 L \\
• z = \sqrt [ 3 ] { 0.065 } \approx 0.134 L
• \end{array}\)
• B) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.015 } \approx 0.2466 L
• \end{array}\)
• C) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.065 } \approx 0.402 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.055 } \approx 0.380 L
• \end{array}\)
• D) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.025 } \approx 0.292 L \\
• y = \sqrt [ 3 ] { 0.035 } \approx 0.327 L \\
• z = \sqrt [ 3 ] { 0.115 } \approx 0.486 L
• \end{array}\)
• E) \(\begin{array} { l }
• x = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• y = \sqrt [ 3 ] { 0.165 } \approx 0.548 L \\
• z = \sqrt [ 3 ] { 0.265 } \approx 0.642 L
• \end{array}\)

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Definitions:

Discounted Payback

A capital budgeting method that calculates the time required to recoup an investment based on discounted cash flows.

Stockholder Wealth

The total value of all financial assets owned by the shareholders of a company, often measured by the market value of the shares held.

Net Present Value

A method used in capital budgeting to evaluate the profitability of an investment or project, considering the time value of money.

Project

A temporary endeavor undertaken to create a unique product, service, or result with defined beginning and end.