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 (dont 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 function and constraints. (Hint: the number of variables will double and each path is represented by a variable). Use data provided in question 2.