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A trucking firm must transport exactly 900,800,700, and 1,000 units of a product to four cities: A, B, C, D. The product is manufactured and supplied in two other cities, X and Y, in the exact amounts to match the total demand. The production of units from the two cities is 1,900 and 1,500 units, respectively to X and Y. The cost per unit to transport the product between the manufacturing plants in cities X and Y and the demand market cities A,B,C,D are given here:
Demand market
Supply Plant A B C D
x .65 .70 .80 .90
y .60 .60 .80 .70
For example in the table , 40.65 is the cost to ship one unit from supply plant x to demand market a. The trucking firm needs to know how many units should be shipped from each supply city to each demand city in such a way that it minimizes total costs. What is the LP model formulation for this problem.
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