Part A$.$ Please read the scenario $1($below$)$ and formulate the problem by hand $($don$\text{'}$t solve$).$ To understand how to formulate the problem see the following example.

Define variables.

Define the objective function.

Define the respective constraints.

Scenario: $1.$ You have just got a $$150,000$ inheritance from a well$-$off aunt. However, she knows that you might not have the best judgment in terms of money matters. As such, you must invest all the money $($cannot spend any on parties or vacations$).$ Also, stipulated is that you cannot spend more than $10\%$ of the funds on "crazy" investments, while "hot" shares cannot exceed $30\%.$ Finally, "sleepy" investments should at a minimum be $30\%$ of the portfolio. Of course, you would like to maximize how much money you will make.

Here is a classification of shares

Shares

Bit coin

Doll Crafters

Bio$-$medical

Dow

Dow

Utilities

Expected ROI $\%$

$25$

$17$

$13$

$10$

$7$

Classification

Crazy

Hot

Mild

Sleepy

Sleepy