$(14$ points total$)$

$3.$ A manufacturer produces goods at five US cities, from which the goods are sent to seven major customers in the following cities: Fillmore, Grant, Hayes, Jefferson, Kennedy, Lincoln and Madison. The monthly production capacity of the goods is shown in the table below:

$\backslash$table$[[$Manufacturing Cities,$\backslash$table$[[$Monthly Production$],[$Capacity $($tons$)]]],[$Adams$,900],[$Boston$,900],[$Carter$,800],[$Deston$,750],[$Elmira$,850]]$

The monthly demands for each customer $($in tons$)$ are shown below.

$\backslash$table$[[,$Fillmore,Grant,Hayes,Jefferson,Kennedy,Lincoln,Madison$],[$Demand$,300,400,200,400,500,200,300]]$

The shipping costs per ton of product from the manufacturers to the customers are shown in the table below.

Shipping costs per ton $($$$)$ :

$\backslash$table$[[$From$/$to$,$Fillmore,Grant,Hayes,Jefferson,Kennedy,Lincoln,Madison$],[$Adams$,200,120,140,100,100,70,90],[$Boston$,90,70,130,90,160,140,160],[$Carter$,100,120,150,180,120,120,150],[$Deston$,180,100,110,70,140,80,110],[$Elmira$,50,110,100,60,80,150,120]]$

a$)$ Solve a Transportation Problem in Excel to find the lowest cost delivery plan to meet the customers' requirements.

$($i$)$ Report the minimum cost from your solution.

$($ii$)$ Insert $($paste$)$ below the Excel spreadsheet that you used showing the optimal solution. $($include all rows and columns of the spreadsheet$)$

$($i$)$ Minimum cost $=$

$($ii$)--$ Paste Your Excel Spreadsheet Here $--$

b$)$ How much does Boston send to each destination?

c$)$ From which manufacturing cities does Lincoln receive shipments $-$ and how many tons are sent from each?