Harvest Hope owns $7$ box trucks, each truck has a $20$ ton capacity. The trucks are distributed among all of their warehouses, $3$ trucks serve the Greenville Warehouse, $2$ Trucks serve the Columbia warehouse, and $2$ trucks serve the Florence warehouse. On a weekly basis, Greenville Warehouse receives $50$ tons worth of goods to dispatch to other warehouses, Columbia warehouse receives $35$ tons to dispatch to other warehouses and Florence receives $30$ tons to dispatch to other warehouses.

The cost per trip for supplying each of the warehouses from each of the processing locations is shown in the following table.

CITY GREENVILLE COLUMBIA FLORENCE

GREENVILLE $$-$ $$400\mathrm{.}00$ $$900\mathrm{.}00$

COLUMBIA $$400\mathrm{.}00$ $$-$ $$500\mathrm{.}00$

FLORENCE $$900\mathrm{.}00$ $$500\mathrm{.}00$ $$-$

Due to limited amount of personnel, Greenville warehouse can only process $40$ tons per week of incoming goods, Columbia warehouse can process $40$ tons per week as well, and Florence warehouse can only process $30$ tons per week

a$.$ Formulate an LP model for this problem.

b$.$ Implement the model in a spreadsheet and solve it$.$

c$.$ What is the optimal solution?

d$.$ Is the optimal solution degenerate?

e$.$ Is the optimal solution unique? If not, identify an alternate optimal solution for the problem.