Chapter 2.1, Problem 97AYU

Cost of Transatlantic Travel A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost $C$ (in dollars) per passenger is given by

$C\left(x\right)=100+\frac{x}{10}+\frac{36,000}{x}$

where $x$ is the ground speed (airspeed $\pm$ wind).

a. What is the cost per passenger for quiescent (no wind) conditions?

b. What is the cost per passenger with a head wind of 50 miles per hour?

c. What is the cost per passenger with a tail wind of 100 miles per hour?

d. What is the cost per passenger with a head wind of 100 miles per hour?

To determine

To find:

1. The cost per passenger for quiescent conditions.
2. cost per passenger with a head wind of 50 miles per hour.
3. the cost per passenger with a tail wind of 100 miles per hour.
4. cost per passenger with a head wind of 100 miles per hour when the cost function per passenger is given by $C\left(x\right)=100 + \frac{x}{10} + \frac{36,000}{x}$, where $x$ is the $\text{ground speed }\left(\text{airspeed ± wind}\right)$.

Answer to Problem 97AYU

a) $\$222$; b) $\$225$; c) $\$220$; d) $\$230$

Explanation of Solution

Given:

$C\left(x\right)=100 + \frac{x}{10} + \frac{36,000}{x}$ where $x$ is the $\text{ground speed }\left(\text{airspeed ± wind}\right)$ and $\text{airspeed = 500 miles per hour}$ and cost in dollars.

Calculation:

$C\left(x\right)=100 + \frac{x}{10} + \frac{36,000}{x}$

a) when $x = 500$ $\left(\text{no wind}\right)$

$C\left(500\right)=100 + \frac{500}{10} + \frac{36,000}{500}$

$=100+ 50+72$

$=\$222$

b) when $x = 450\left(500-50\right)$

$C\left(450\right)=100+ \frac{450}{10} + \frac{36,000}{450}$

$=100+45+80$

$= \$225$

c) when $x = 600\left(500+100\right)$

$C\left(600\right)=100 + \frac{600}{10} + \frac{36,000}{600}$

$=100+60+60$

$=\$220$

d) when $x = 400\left(500-100\right)$

$C\left(400\right)=100 + \frac{400}{10} + \frac{36,000}{400}$

$=100+40+90$

$=\$230$