A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below.

Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel.
(a) Formulate a linear programming model for this problem. Using the Big M method, construct the initial simplex tableau ready to apply the simplex method (but do not actually solve).
(b) Now formulate this problem as a transportation problem by constructing the appropriate parameter table. Compare the size of this table (and the corresponding transportation simplex tableau) used by the transportation simplex method with the size of the simplex tableaux from part (a) that would be needed by the simplex method.

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Hauling Cost per Ton at Site Pit 2 3 Price per Ton $300 North $100 190 $160 South 180 110 140 420