A soot-spewing factory that produces steel windows is next to a laundry. Assume that the factory faces a prevailing market price ofPX= $40. Its total cost function isC=X2,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 isC=Y2+ 0.05X, whereYis pounds of laundry washed. The demand curve faced by the laundry is perfectly elastic at a price atPY= $10 per pound.

1. (a)What outputsXandYwould maximize the sum of the profits of these two firms? Assume the two firms were run by the same management.
2. (b)What are competitive market outputs ofXandY?
3. (c)What per-unit tax would we need to set on window production to obtain the outputs found in part a of this problem?