Try It Yourself

Try It Yourself#

Exercise 1#

Marginal revenue

The weekly demand for Math-Hero video games is given by

\[p=x^3−150x+1000\]

where $x$ is the number of video games produced and sold, and $p$ is in dollars. Using the marginal revenue function, $R'(x)$, approximate the marginal revenue when 10 Math-Hero video games have been produced and sold and interpret the result.

Exercise 2#

Marginal revenue

The weekly demand for Math Wars - Return of the Calculus video games is given by

\[p= \frac{250}{x-5} + 3500\]

where $x$ is the number thousands of video games produced and sold, and $p$ is in dollars.

Using the marginal revenue function, $R'(x)$, approximate the marginal revenue when 10,000 video games have been produced and sold and interpret the result.

Exercise 3#

Marginal average cost

The daily cost (in dollars) of producing LCD ultra-high definition televisions is given by

\[C(x)= 5x^3 - 50x^2 + 50x + 2500\]

where $x$ denotes the number of thousands of televisions produced in a day.

Using the marginal average cost function, $\overline{C}'(x)$, approximate the marginal average cost when 5000 televisions have been produced and interpret the result.

Exercise 4#

Elasticity of demand

Given the demand equation $p + \dfrac{x}{5} = 40$, where $p$ represents the price in dollars and $x$ the number of units, determine the elasticity of demand when the price $p$ is equal to $20 and interpret the result.

Exercise 5#

Elasticity of demand

The demand for a product is given by

\[f(p) = 6 + \dfrac{7}{p}.\]

Determine the elasticity when $p = 3$ and interpret the result.

Exercise 6#

Unitary demand

Given the demand equation $p = 12 - \dfrac{x^2}{25}$, determine the price $p$ at which demand is unitary.

Exercise 7#

Maximum revenue

Given the demand equation $p + 5x = 20$, determine the price $p$ at which total revenue is maximized.