28 Thailand inducts naval draftees at three drafting centers. Then the draftees must each be sent to one of three naval bases for training. The cost of transporting a draftee from a drafting center to a base is given in Table 26. Each year, 1,000 men are inducted at center 1; 600 at center 2;

and 700 at center 3. Base 1 can train 1,000 men a year, base 2, 800 men; and base 3, 700 men. After the inductees are trained, they are sent to Thailand’s main naval base (B).

They may be transported on either a small ship or a large ship. It costs $5,000 plus $2 per mile to use a small ship. A small ship can transport up to 200 men to the main base and may visit up to two bases on its way to the main base. Seven small and five large ships are available. It costs $10,000 plus

$3 per mile to use a large ship. A large ship may visit up to

three bases on its way to the main base and may transport up to 500 men. The possible “tours” for each type of ship are given in Table 27.
Assume that the assignment of draftees to training bases is done using the transportation method. Then formulate an IP that will minimize the total cost incurred in sending the men from the training bases to the main base. (Hint: Let yij number of men sent by tour i from base j to main base (B) on a small ship, xij number of men sent by tour i from base j to B on a large ship, Si number of times tour i is used by a small ship, and Li number of times tour i is used by a large ship.)

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TABLE 26 Te ($) From Base 1 Base 2 Base 3 Center 1 200 200 300 Center 2 300 400 220 Center 3 300 400 250 $Based on Choypeng, Puakpong, and Rosenthal (1986).