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1] [3i] air] A soot-spewing factory that produces steel is next to a laundry. The Factor};r faces a prevailing market price ofP=$Eii}. Its cost function is [2:19, where X is the steel output Suppose each unit of steel pro duced produces two units of soot [S], that is, S = 2): The laundry produces clean wash. which it hangs out to dry. The soot from the steel Factoryr smu dges the washr so that the laundry has to protect the wash from the soot of the factory and this increases its co sis of p ro ducing clean clothes. The cost function for the laundry is C = F2 "' Y2 +{1_;'B] "' 33. where Y is pounds of Ian ndrv washed. it pound of clean laundry sells for $311 Both rms face a competitive market a] Compute the outputs of steel and laundry that would maximize the sum of the prots of these two rms. How much are joint prots? b] Calculate the Pigouvian tax. c] illustrate the Pigouvian tax and tax revenue in a graph with soot on the :4:- aXis and $ on the v-aais