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# A steel firm creates water pollution for a downstream fishery. The price and cost functions for steel and fish are as follows:

A steel firm creates water pollution for a downstream fishery. The price and cost functions for steel and fish are as follows:

Price of steel 30

Cost function for steel Csteel(s,x) 6s + 3s2 - 20x + 2x2

Price of fish 50

Cost function for fish Cfish(f,x) 20f+5f2 + 14x + x2

(a) How much steel (s) and pollution (x) will the steel plant produce if operated independently? (It will maximise profit)

(b) How much fish (f) will the fishery produce if operated independently? (Again, it wants to maximise profit)

(c) How much steel (s), pollution (x) and fish (f) will the steel and fish plants produce if they are merged and act to maximize joint profit? (Maximise joint profit)