Chapter 1.2, Problem 35E

Demand: Smartphones The worldwide demand for smartphones may be modeled by

$q\left(p\right)=0.17p^2-63p+5,900$ million units sold annually $\left(100\le p\le 200\right)$, where p is the unit price in dollars.²⁷

a. Use the demand function to estimate, to the nearest million units, worldwide sales of smartphones if the price is $110.

b. Extrapolate the demand function to estimate, to the nearest million units, worldwide sales of smartphones if the price is $90.

c. Model the worldwide annual revenue from the sale of smartphones as a function of unit price, and use your model to estimate, to the nearest billion dollars, worldwide annual revenue when the price is set at $110.

[Hint: $\text{Revenue}=\text{Price×Quantity}=p\cdot q\left(p\right)$

]

d. Graph the function you obtained in part (c). According to the graph, does worldwide revenue increase or decrease as the price decreases past $110?