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A company uses four special tank trucks to deliver four different gasoline products to customers. Each tank has five compartments with different capacities: 500,750,1200,1500, and 1750 gallons. The daily demands for the four products are estimated at 10,15,12, and 8 thousand gallons. Any quantities that cannot be delivered by the company’s four trucks must be subcontracted at the additional costs of 5,12,8, and 10 cents per gallon for products 1,2,3, and 4, respectively. Develop the optimal daily loading schedule using an ILP for the four trucks that will minimize the additional cost of subcontracting. (Define xt,p,c as the number of gallons of product p in compartment c at time t and yt,p,c as a binary variable that is equal to 1 when compartment c is used for product p at time t and zero otherwise and wp to be the amount in gallons subcontracted for product p).
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