91Ó°ÊÓ

Cost of Trans-Atlantic 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$Â\pm$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?

We have to find the cost per passenger for quiescent (no wind) conditions.

We know the value of $x=(\mathrm{airspeed}Â\pm \mathrm{wind})$

In no wind conditions the value of wind$=0$

$$\begin{gathered} C\left(500\right)=100+\frac{500}{10}+\frac{36,000}{500} \\ C\left(500\right)=100+50+72 \\ C\left(500\right)=222 \end{gathered}$$

The value of $x=(\mathrm{airspeed}Â\pm \mathrm{wind})$

We have to find a head wind of 50 miles per hour.

So the value of

$$\begin{gathered} x=500-50 \\ x=450 \end{gathered}$$

$$\begin{gathered} C\left(450\right)=100+\frac{450}{10}+\frac{36,000}{450} \\ C\left(450\right)=100+45+80 \\ C\left(450\right)=225 \end{gathered}$$

The value of$x=(\mathrm{airspeed}Â\pm \mathrm{wind})$

We have to find a tail wind of 100 miles per hour.

So the value of

$$\begin{gathered} x=500+100 \\ x=600 \end{gathered}$$

$$\begin{gathered} C\left(600\right)=100+\frac{600}{10}+\frac{36,000}{600} \\ C\left(600\right)=100+60+60 \\ C\left(600\right)=220 \end{gathered}$$

The value of$x=(\mathrm{airspeed}Â\pm \mathrm{wind})$

We have to find a head wind of 100 miles per hour.

So the value of

$$\begin{gathered} x=500-100 \\ x=400 \end{gathered}$$

$$\begin{gathered} C\left(400\right)=100+\frac{400}{10}+\frac{36,000}{400} \\ C\left(400\right)=100+40+90 \\ C\left(400\right)=230 \end{gathered}$$