There are two factories in a small town. Both of them emit carbon dioxide into the air. Factory 1 currently emits 120 tons per month, whereas factory 2 currently emits 160 tons per month. The technology of each factory is dierent, so their costs of reducing emissions are dierent as well. The tables below show the costs of reducing emissions in increments of 20 tons per month for each factory: Factory 1 Total cost of reducing emissions by 20 tons/month: $50 Total cost of reducing emissions by 40 tons/month: $150 Total cost of reducing emissions by 60 tons/month: $270 Total cost of reducing emissions by 80 tons/month: $410 Total cost of reducing emissions by 100 tons/month: $570 Factory 2 Total cost of reducing emissions by 20 tons/month: $20 Total cost of reducing emissions by 40 tons/month: $60 Total cost of reducing emissions by 60 tons/month: $110 Total cost of reducing emissions by 80 tons/month: $200 Total cost of reducing emissions by 100 tons/month: $300 The existing technology does not allow for reductions in emissions beyond 100 tons/month. That is, the most each factory could reduce its emissions by is 100 tons/month. Suppose the government in this town would like to cut monthly emissions to half of the current level. To do that, the government has decided to impose a tax for every 20 tons of pollution per month emitted by a factory. To achieve its desired goal (but not exceed the goal), the tax would have to be set between $X and $Y for every 20 tons/month. (The rst number should be the lower end of the tax, and the second number should be the higher end of the tax.) What is the value of $X