1) Formulate the initial simplex tableau for the XYZ Sawmill Company. 2) Use the North-West Comer Rule to find an initial feasible basic solution. Is it optimal? What is the total cost of this solution? 3) Use the smallest-Cost Rule to find an initial feasible basic solution. Is it optimal? What is the total cost of this solution? 4) Solve the transportation problem by using the initial solution in 3). The XYZ Sawmill Company's CEO asks to see next month's log hauling schedule to his three sawmills. He wants to make sure he keeps a steady, adequate flow of logs to his sawmills to capitalize on the good lumber market. Secondary, but still important to him, is to minimize the cost of transportation. The harvesting group plans to move to three new logging sites. The distance from each site to each sawmill is in Table 1. The average haul cost is $2 per mile for both loaded and empty trucks. The logging supervisor estimated the number of truckloads of logs coming off each harvest site daily. The number of truckloads varies because terrain and cutting patterns are unique for each site. Finally, the sawmill stimated the truckloads of logs their mills need each day. All these estimates are in Table 1. Table 1.-Supply and demand of sawlogs for the XYZ Sawmill Company. Logging Distance to mill (miles) Maximum truckloads./day Site Mill A Mill B Mill C per logging site 50 10 17 26 Mill demand (truckloads day) 30 The next step is to determine costs to haul from each site to each mill (Table 2). Table 2-Round-trip transportation costs for XYZ Sawmill Company Logging Mill A Mill B Mall c $ 32 $ 60 $ 200 40 68 site SO 120 104 *(8 miles x 2) (52 per mile) = $32 We can set the LP problem up as a cost minimization: that is we want to minimize hauling costs and meet each of the sawmills daily demand while not exceeding the maximum number of truckloads from each site