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ADVANCED MATH
Translate the following arguments into symbolic form and use the first four rules of inference to derive the conclusion of each. The letters to be used for the simple statements are given in parentheses after each exercise. Use these letters in the order in which they are listed. Either we take recycling seriously or we will be buried in garbage. If we incinerate our garbage only if our health is jeopardized, then we do not take recycling seriously. If our landfills are becoming exhausted, then if we incinerate our garbage, then toxic ash will be produced. If toxic ash is produced, then our health is jeopardized. Our landfills are becoming exhausted. Therefore, we will be buried in garbage. (R, B, I, H, L, T )
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Oilco has oil fields in San Diego and Los Angeles. The San Diego field can produce 500,000 barrels per day, and the Los Angeles field can produce 400,000 barrels per day. Oil is sent from the fields to a refinery, in either Dallas or Houston (assume each refinery has unlimited capacity). To refine 100,000 barrels costs $700 at Dallas and$900 at Houston. Refined oil is shipped to customers in Chicago and New York. Chicago customers require 400,000 barrels per day, and New York customers require 300,000 barrels per day. The costs of shipping 100,000 barrels of oil (refined or unrefined) between cities are shown in Table 35. a. Formulate an MCNFP that can be used to determine how to minimize the total cost of meeting all demands. b. If each refinery had a capacity of 500,000 barrels per day, how would the part (a) answer be modified? TABLE 35: $$ \begin{matrix} \text{From} & \text{To (\$)}\\ \text{ } & \text{Dallas} & \text{Houston} & \text{New York} & \text{Chicago}\\ \text{Los Angeles} & \text{300} & \text{110} & \text{—} & \text{—}\\ \text{San Diego} & \text{420} & \text{100} & \text{—} & \text{—}\\\text{Dallas} & \text{—} & \text{—} & \text{450} & \text{550}\\ \text{Houston} & \text{—} & \text{—} & \text{470} & \text{530}\\ \end{matrix} $$
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