A fisherman from nearby Newton Town has equipment that allows him to collect fish in Leibniz Bay once a day until 11pm. That is, he may cast his net one time and instantly catch his fish for the day.

He wants to pick the best time to go fishing in order to maximize his income.

We know each ton of salmon sells for $4000, and each ton of herring sells for $3000.

Based on the ichthyologist's ongoing research, the numbers of tons of fish caught in the net by the fisherman, at the instant he casts his net, if cast at time t are:

fs(t)=0.1S(t)=0.1(41t26t+46) and fH(t)=0.1H(t)=0.1(361t31211t2+8t+30)

B) Construct a function, y = P(t), that represents the amount of money the fisherman makes by casting his net one time at time t in [0, 23], given the information above. Simplify the function.

C) Use this function, y = P(t), to determine the time at which the fisherman should cast his net in order to maximize the amount of money made when selling the fish he catches.

Note: The fisherman may cast his net at t = 23 hours or 11pm, but not an instant after.

D) At what time should the fisherman avoid casting his net? That is, when would his profit be minimized?