For the given transportation problem:

To

From

A

B

C

Supply

X

$$$$10$

$$$$19$

$$$$12$

$100$

Y

$$$$17$

$$$$13$

$$$$9$

$150$

Z

$$$$20$

$$$$18$

$$$$14$

$505$

Demand

$80$

$120$

$70$

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

unbalanced

b$)$ Before finding the initial$$ solution, a

dummy destination node

should be introduced.

c$)$ The total cost of the initial solution developed using the intuitive$$ lowest$-$cost method$$ will be

$3190$

d$)$ The total cost of the optimal solution$=$