You have just got a $100,000 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	Expected ROI %	Classification
Bit coin	25	Crazy
High-tech	15	Hot
bio-medical	18	Hot
Dow	10	Mild
Utilities	7	Sleepy

Please formulate the problem (don’t solve). Please write by hand (see as an example Financial 2 (by hand)).

Define variables.

Define the objective function.

Define the respective constraints.

You and your classmate from Quant 2020 have decided to open a zip ice-cream service. Factories are located in Black Forest, Cimarron Hills, Knob Hills and Security-Widefield. Your retail outlet shops are located in Fountain, Garden of the Gods, and Briargate. Your business is charged by pint mile at a rate of $ .02 per mile per pint.

Locate the distances between the four factories and retail shops (use google maps and just take a central location). Compute the cost for each shipping route per pint.

There are certain production constraints:

Factory	Capacity (pints)
Cimarron Hills	500
Knob Hills	700
Black Forest	1000
Security-Widefield	400

There are certain demands which need to be met:

Shop	Demand (pints)
Fountain	600
Garden of the Gods	600
Briargate	1200

You want to minimize your shipping costs, while ensuring that the demands are met subject to capacity limits of the respective ice-cream factories.

Please formulate the problem (don’t solve). Please write by hand (see Transportation 2 (by hand)).

Define variables.

Define the objective function.

Define the respective constraints.

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3.

There is the possibility to add two warehouses in your transportation model. The warehouses are at the intersection of I-25 & monument and I-25 & 24 respectively (use google maps to get new distances). There are no capacity constraints in the warehouses. All supplies need to travel though the warehouses between factory and retail store. You will only need to traverse through a single warehouse (i.e. no intra-warehouse transfers). Redefine variables, objective functions and constraints. (Hint: the number of variables will double and each path is represented by a variable). Use the data provided in question 2.