1. (8 points) A rectangular piece of land is to be fenced using two kinds of fencing. Two opposite sides will be fenced using standard fencing that costs $6/m, while the other two sides will require heavy-duty fencing that costs $9/m. What are the dimensions of the rectangular lot of greatest area that can be fenced for a cost of $9000?2. (1 1 points) Lily operates a successful bake shop. One of her specialties is a very delicious moon cake. She buys the moon cakes from a supplier who charges $6.00 per cake. and she sell 200 cakes weekly for $10.00 each. Research shows that profit from the moon cake sales can be increased by increasing the price. Unfortunately, for every increase of $0.50 cents, sales will drop by seven cakes. What price should Lily sell the moon cakes for to obtain a maximum weekly profit?3. (20 points) Determine the derivatives for each function below. (a) /(x) = 10e-32 (d) g(x) = 82345 (e) q(x) =1.93 + 719 (b) y = since -e (c) h(x) = (x-ez)4. (14 points) The number of rabbits in a forest at time {, in months, is /() = 500[10 + e-wh ] (a) What is the initial number of rabbits in the forest? (b) Determine the rate of change of the number of rabbits at time f. (c) How fast is the number of rabbits changing after one year? (d) Determine the largest number of rabbits in the forest during the first three years. (e) Using graphing technology, sketch Ivs t below. Give physical reasons why the population of rabbits might behave this way