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Suppose There Are Three Power-Generating Plants, Each of Which Has

question 56

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Suppose there are three power-generating plants, each of which has access to 5 different production processes. The table below summarizes the cost of each production process and the corresponding number of tons of smoke emitted each.  Process  A  B  C  D  E  (smoke/day)   (4 tons/day)   (3 tons/day)   (2 tons/day)  (1 ton/day)   (0 tons/day)   Cost to Firm X($/ day)  $500$514$530$555$585 Cost to Firm Y ($/day)  $400$420$445$480$520 Cost to Firm Z($/day)  $300$325$360$400$550\begin{array}{|c|c|c|c|c|c|}\hline \text { Process } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\text { (smoke/day) } & \text { (4 tons/day) } & \text { (3 tons/day) } & \text { (2 tons/day) } & (1 \text { ton/day) } & \text { (0 tons/day) } \\\hline \text { Cost to Firm } X(\$ / \text { day) } & \$ 500 & \$ 514 & \$ 530 & \$ 555 & \$ 585 \\\hline \text { Cost to Firm Y (\$/day) } & \$ 400 & \$ 420 & \$ 445 & \$ 480 & \$ 520 \\\hline \text { Cost to Firm Z(\$/day) } & \$ 300 & \$ 325 & \$ 360 & \$ 400 & \$ 550 \\\hline\end{array}
Suppose the government decides to impose a tax on each ton of smoke emitted. What would be the lowest tax, in whole dollars, that would reduce emissions to 6 tons per day?


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