An automotive company produces its new model in three manufacturing plants

located in California, Mexico and Michigan. The car agents receive cars from the

distribution centres located in Arizona, lowa and South Carolina. The anticipated

production over the next month $($in $100$ s of cars$)$ is $150$ at California, $175$ at Mexico

and $275$ at Michigan. Based on the sales records and other factors, the automotive

company decided that the following numbers of cars $($in $100$ s of cars$)$ at the

distribution centres at the month's end: $200$ at Arizona, $100$ at Iowa and $300$ at South

Carolina. The cost of shipping from each manufacturing plant to each distribution

centre is given in Table $3($in $$1,000$ s$)$

Table $3_{?}$

$($i$)$ Is this an unbalanced transportation problem, explain why?

$($ii$)$ Determine a pattern of shipping that minimizes the total transportation cost

from the manufacturing plants to the distribution centres by using the greedy

heustic.