Solve the Problem $\mathrm { V } ( \mathrm { x } ) = \mathrm { x } ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )$

question 107

Multiple Choice

Solve the problem.
-A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 11 inches by 27 inches by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.

• A) \(\mathrm { V } ( \mathrm { x } ) = \mathrm { x } ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )\)
• B) \(\mathrm { V } ( \mathrm { x } ) = ( 11 - 2 \mathrm { x } ) ( 27 - 2 \mathrm { x } )\)
• C) \(V ( x ) = ( 11 - x ) ( 27 - x )\)
• D) \(V ( x ) = x ( 11 - x ) ( 27 - x )\)

---

Definitions:

Certainty Equivalent NPV

A method that adjusts the net present value (NPV) of an investment by incorporating the decision maker's risk aversion, providing a risk-adjusted NPV under certainty.

Traditional NPV

Net Present Value; a method of evaluating the profitability of an investment by calculating the present value of expected future cash flows minus the initial investment cost.

Beta

A measurement of the volatility of a stock or a portfolio in comparison to the market as a whole.

Discount Rate

The rate employed in discounted cash flow assessments to establish the current valuation of anticipated future cash flows.