Solve the Problem $R ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x$

question 49

Essay

Solve the problem.
-Given $R ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 2 x$ and $C ( x ) = 2 x ^ { 2 } + 24$ where $x$ represents the number of items produced in hundreds, $R( \mathrm { x } )$ and $\mathrm { C } ( \mathrm { x } )$ represent revenue and cost in thousands of dollars. where x represents the number of items produced in hundreds, R(x)
a)Find P(x).
b)Find P(0), R(0), and C(0)and interpret each of these.
c)Find the break-even point (value wherehere $P ( x ) = 0 ) \text { if } 0 < x < 4 \text {. }$ d)For what values of x ist values of x is $\mathrm { P } ( \mathrm { x } ) > 0 \text { if } 0 < x < 4 ?$ e)For what values of x ist values of x is $P ( x ) < 0 \text { if } 0 < x < 4 ?$ f)Interpret the results from parts d)and e).

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Definitions:

Return on Investment

A measure used to evaluate the efficiency of an investment, calculated by dividing the profit earned on an investment by the cost of that investment.

Controllable Margin

The portion of profit or margin that can be directly influenced by management decisions and actions.

Operating Assets

Assets used in the daily operations of a business to generate revenue, including cash, inventory, and equipment.

Return on Investment

A performance measure used to evaluate the efficiency of an investment or compare the efficiencies of several different investments.