If a facility is decided to be opened in a region, its capacity is determined beforehand and is given in Table $3.$

Table $3$:

$\backslash$table$[[$Region$,$Capacity in tons$],[$A$,225],[$B$,500],[$C$,300],[$D$,900],[$E$,600],[$F$,130],[$G$,110]]$

The final key body of data involves the fixed costs of opening a facility in each region. The fixed cost of setting up a facility is different in each region as shown in Table $4.$

Table $4$:

$\backslash$table$[[,$A$,$B$,$C$,$D$,$E$,$F$,$G$],[$Fixed Cost,$1000,1500,1200,2500,1800,800,750]]$

The objective is to determine the overall distribution plan that minimizes the total annual cost.

You are the head of the OR team that has been assigned the task of determining the shipping plan for each of the following options.

Option $1$: The new facilities are opened in region B$,$ C$,$ and F$.$

Option $2$: The new facilities are opened in region A$,$ D$,$ and F$.$

Option $3$: The new facilities are opened in region A$,$ E$,$ and G$.$

Analyze the company's distribution strategy and suggest possible improvements.

You should answer the following questions when you work on the case:

Question $1.$ Present your results for each of the three options. $(40$ pts $)$

Hint: Optimize the distribution plan by formulating and solving a linear programming model for each option. Develop three distribution plans that minimizes total shipping and fixed costs while satisfying demands at the regions $($Use GAMS to develop the models$).$ Discuss the resulting benefits of the suggested plans.