$2.)$ Global rice production and consumption are highly concentrated in Asia, where rice is a basic staple for most of its inhabitants. Around $90\%$ of world rice is produced and consumed in the region. Rice continues to be the most important commodity in the Philippines, accounting for about $15\%$ of gross value added in agriculture. It is grown in nearly two$-$thirds of the country$$s arable land and is a major source of livelihood of many small farmers and agricultural landless households David & Balisacan,$1995).$ The country$$s palay production increased from $15\mathrm{.}77$ million in $2010$ mt to $18\mathrm{.}97$ million mt in $2014.$ Production grew by an average annual rate of $4\mathrm{.}7$ percent over the last five $(5)$ years. Total harvest area expanded from $4\mathrm{.}35$ million hectares in $2010$ to $4\mathrm{.}74$ million hectares in $2014.$ Palay production in $2014$ reached $18\mathrm{.}97$ million mt$,2\mathrm{.}8$ percent or $0\mathrm{.}53$ million mt higher than the $18\mathrm{.}44$ million mt output level in $2013.$ Area harvested slightly contracted from $4\mathrm{.}75$ million hectares in $2013$ to $4\mathrm{.}74$ million hectares in $2014$ or by $0\mathrm{.}1$ percent. The following data on Table $1$ show the demand, supply, and surplus$/$deficit of rice in the Ilocos Region, Cordillera Administrative Region, Cagayan Valley, Central Luzon, and CALABARZON Region. The table on the next page summarizes the supply from the major rice producers in Luzon as well as the demand of each of the regions in Luzon. The table also shows the distances in kilometers between the regions to be able to determine the cost. The cost of delivery is obtained through the Php $8\mathrm{.}00$ per kilometer of a $12\mathrm{.}5$ metric ton truck which is an estimated price for delivery set by the Philippine Statistics Authority $($PSA website, n$.$d$.)$ Determine the minimum total transportation cost $($in terms of distance$)$ and Total minimum cost $($at Php $8\mathrm{.}00$ per kilometer for every $12\mathrm{.}5$ metric ton truck$)$ using $($a$)$ The Northwest Corner Cell Method, $($b$)$ The Least Cost Method, and $($c$)$ The Vogel$$s Approximation Method. Finally, describe and compare the results of these methods.