$6\mathrm{.}9$ The table below shows the flows in an optimal solution for a Transportation Problem withShown below is the data for a Transportation Problem with $3$ origins $($Bear River, Elko, and

Wasatch$)$ and $4$ destinations. The supply at each origin, demand at each store, and the unit

costs are shown in the following table.

a$.$ Solve the Transportation Problem to find the minimum cost shipping pattern.

Minimum Cost $=$

$$380$

Fill in the table with the optimal flows:

b$.$ Which origins, if any, send all of their supply?

Bear River and Wasatch

c$.$ Suppose now that Dest $4$ must receive exactly $50\%$ more from Wasatch than from Elko. Find

the minimum cost shipping pattern.

Minimum Cost $=$

Fill in the table with the optimal flows:

four origins and four destinations, along with the supply and demand. In this solution, is

there unmet demand at any destination? If so$,$ how much and where?