Find an initial solution to the following transportation problem.

$$

$$

To

From

A

B

C

Supply

X

$$$$1010$

$$$$1919$

$$$$1212$

$150150$

Y

$$$$1717$

$$$$1313$

$$$$99$

$150150$

Z

$$$$2020$

$$$$1818$

$$$$1414$

$7070$

Demand

$120120$

$8080$

$6060$

Part $2$

Based on the given demand and$$ supply, the given transportation problem is

unbalanced

$.$

Part $3$

Before finding the initial$$ solution, a dummy

destination

should be introduced.

Part $4$

The starting solution using$$ northwest$-$corner method$$ is:

Part $5$

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

To

From

A

B

C

Dummy

Supply

X

$$$$1010$

$$$$1919$

$$$$1212$

$0$

$150150$

$120120$

$00$

$00$

$110110$

Y

$$$$1717$

$$$$1313$

$$$$99$

$0$

$150150$

$00$

enter your response here

enter your response here

enter your response here

Z

$$$$2020$

$$$$1818$

$$$$1414$

$0$

$7070$

$00$

enter your response here

enter your response here

enter your response here

Demand

$120120$

$8080$

$6060$

Part $6$

$$a$)$ The total cost of the initial solution developed using the$$ northwest$-$corner method$=$

$$$enter your response here.

Part $7$

The starting solution using the intuitive$$ lowest$-$cost method$$ is:

Part $8$

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

To

From

A

B

C

Dummy

Supply

X

$$$$1010$

$$$$1919$

$$$$1212$

$0$

$150150$

enter your response here

enter your response here

enter your response here

enter your response here

Y

$$$$1717$

$$$$1313$

$$$$99$

$0$

$150150$

enter your response here

enter your response here

enter your response here

enter your response here

Z

$$$$2020$

$$$$1818$

$$$$1414$

$0$

$7070$

enter your response here

enter your response here

enter your response here

enter your response here

Demand

$120120$

$8080$

$6060$