Consider the transportation table below. The solution displayed was obtained by performing some iterations of the transportation method on this problem.

$$

Destination

Source

Denver

Yuma

Miami

Supply

Houston

$$$$2$

$$$$8$

$$$$1$

$25$

$25$

St$.$ Louis

$$$$4$

$$$$5$

$$$$6$

$35$

$10$

$25$

Chicago

$$$$6$

$$$$3$

$$$$2$

$45$

$10$

$35$

Demand

$35$

$35$

$35$

Part $2$

The total cost of the current solution provided$=$$

$$

enter your response here.

Part $3$

Using stepping stone$$ method, to perform an improvement$$ iteration, the improvement index for the unused cell will$$ be:

Part $4$Part $5$Part $6$Part $7$

HoustonminusYumaequals

$$

enter your response here

HoustonminusMiamiequals

$$

enter your response here

St$.$ LouisminusMiamiequals

$$

enter your response here

ChicagominusDenverequals

$$

enter your response here

Part $8$

Based on the improvement index for each of the unused$$ cells, in the first improvement$$ iteration, unused cell HoustonminusMiami should get an assignment of

$$

enter your response here units.

Part $9$

The improved transportation flow will$$ be:

Part $10$

$($Note: You must enter a shipment in every$$ cell, even if the shipment is$0.)$

To

From

Denver

Yuma

Miami

Supply

Houston

$$$$2$

$$$$8$

$$$$1$

$25$

$$

enter your response here

$$

enter your response here

St$.$ Louis

$$$$4$

$$$$5$

$$$$6$

$35$

$$

enter your response here

$$

enter your response here

Chicago

$$$$6$

$$$$3$

$$$$2$

$45$

$$

enter your response here

$$

enter your response here

Part $11$

The total cost of the improved solution$=$$

$$

enter your response here.