QUESTION ONE (10 MARKS) A company is engaged in a plant distribution study .The plan has four main centers at which end items are assembled .Each center uses, among others, a common part .The part is stored in bins at three locations within the plant .Although alternative locations are being considered for the bins the production manager wishes to determine the best way in which to allocate parts from the existing bins to the four work centers .The criterion selected to evaluate the current layout is a measure of volume of parts multiplied times the distance over which the parts are moved. The table below summarizes the distance (in meters) between each bin and each work center ,the number of parts available in each bin and the number required at each work center. Work center Bin 1 2 3 4 Parts Available 1 25 40 75 20 2,000 2 50 40 65 25 1,500 | 3 25 50 70 40 1,500 Parts required 800 1,200 1,500 1,000 If the objective is to maximize the weighted measure of volume times distance, then: a) Formulate this problem as a transportation model and find the optimal solution b) Solve this problem if exactlyr 500 parts must be delivered to work center 3 from bin 2 and at least 400 from bin 1 to work center 4