Assignment

Last year, a gaming app experimented with a subscription service for a collectring of classic games

$($solitaire$,$ spades, hearts, etc.$).$ The consumer demand for this service was modeled by the equation

$Q(p)=1000e^{-p}{?}^2=p$

where $p$ represents the monthly access price and $q$ represents the number of subscribers. You need

to create a report that answers the following questions:

Determine the price that maximizes the number of subscribers. Give the maximum number of subscribers and the revenue $($price times quantity$)$ for this number of subscribers.

Price$=0\mathrm{.}5$

Subscribers $=1284\mathrm{.}03$

Revenue $=642\mathrm{.}015$

What is the price where the rate of subscribers is at its lowest? Keep in mind this question is asking about the rate of subscribers, not the actual number of subscribers.

Fill in the blank for each of the following statements:

a$."$At a starting price of $$0\mathrm{.}75,$ a $1\%$ increase in price will yield a $q,\%$ decrease in demand. Based on this, the app should consider a starting price higher$/$lower $($pick one$)$ than $$0\mathrm{.}75."$

b$."$At a starting price of $$1\mathrm{.}50,$ a $1\%$ increase in price will yield a $\%$ decrease in demand. Based on this, the app should consider a starting price higher$/$lower $($pick one$)$ than $$1\mathrm{.}50."$

How much should the monthly access price be in order to obtain the maximum monthly revenue? What is the maximum monthly revenue?

Monthly access price $=1$

Maximum Monthly revenue $=1000$

All dollar amounts should be rounded to two decimal places. Number of subscribers should be rounded to nearest whole number. Percentages should be written in their entirety $($carry all decimal places$).$