The following table presents$$ cost$,$ capacity, and demand data for a transportation problem in Jinfeng$$ Yue's furniture company.

$$

$$From$\backslash$To

$1$

$2$

$3$

Capacity

A

$$$$30$

$$$$10$

$$$$5$

$20$

B

$$$$10$

$$$$10$

$$$$10$

$30$

C

$$$$20$

$$$$10$

$$$$25$

$75$

Demand

$40$

$60$

$55$

Part $2$

Set up the appropriate transportation table and find the initial solution using the$$ northwest$-$corner rule. Note that a$$ "dummy" source is needed to balance the problem $($enter your responses as whole$$ numbers$).$

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

$$From$\backslash$To

$1$

$2$

$3$

Capacity

A

$$$$30$

$$$$10$

$$$$5$

$20$

$$

enter your response here

$$

enter your response here

$$

enter your response here

B

$$$$10$

$$$$10$

$$$$10$

$30$

$$

enter your response here

$$

enter your response here

$$

enter your response here

C

$$$$20$

$$$$10$

$$$$25$

$75$

$$

enter your response here

$$

enter your response here

$$

enter your response here

Dummy

$$$$0$

$$$$0$

$$$$0$

$$

$30$

$$

enter your response here

$$

enter your response here

$$

enter your response here

Demand

$40$

$60$

$55$

$155$