Chapter 23, Problem 2RP

Explanation of Solution

Determining which investment strategy is the best:

It is given that the person currently has $100. Each week the user can invest any amount of money he or she currently have in a risky investment. With probability 0.40, the amount the user invest is tripled and with probability 0.60, the amount invested is lost.

First, let us calculate the shipping model for 100 crew members. Hence, the data given will be as follows:

$\begin{array}{l}\text{λ=0}\text{.66 per day }\left(\text{2 ships every 3 days}\right)\\ \text{μ=1 day}\\ \text{Number of servers = 100}\end{array}$

Here, $\text{λ}$ is the average rate of the ships entering the system and $\text{μ}$is the service rate.

In the given MMs Template, the above-mentioned details are entered in the highlighted cells B4:B7 appropriately. The screenshot is as shown below:

Once the above details are entered, click on “Click here” button. We can see that the other details are updated automatically because of the built-in formulas. The screenshot is as shown below:

Now, calculate the shipping model for 70 crew members. Hence, the data given will be as follows:

$\begin{array}{l}\text{λ=1 per day }\\ \text{μ=1}\text{.5 day}\\ \text{Number of servers = 70}\end{array}$

Here, $\text{λ}$ is the average rate of the ships entering the system and $\text{μ}$is the service rate.

In the given MMs Template, the above-mentioned details are entered in the highlighted cells B4:B7 appropriately. The screenshot is as shown below:

Once the above details are entered, click on "Click here” button. We can see that the other details are updated automatically because of the built-in formulas.

The screenshot is as shown below:

It is given that a fixed cost of $30 is incurred on every crew member per day