3. A sootspewing factory that produces steel windows is next to a laundry. Assume that the factory faces a prevailing market price of Px = $40. Its total cost function is C = X 2,where X is window output. The laundry produces clean wash, which it hangs out to dry. The soot from the window factory smudges the wash, so the laundry has to clean it again. This increases the laundry's costs. In fact, the total cost function of the laundry is C = Y2 + 0.05X, where Y is pounds of laundry washed. The demand curve faced by the laundry is perfectly elastic at a price at 133/ = $10 per pound. (a) What outputs X and Y would maximize the sum of the prots of these two rms? Assume the two rms were run by the same management. (b) What are competitive market outputs of X and Y? (c) What perunit tax would we need to set on window production to obtain the outputs found in part a of this