instructions: Introduce the problem first. You may paraphrase the problem statement. Write in complete sentences! You can center important equations, but they should still be part of your narrative flow. Write as if you were explaining the solution to another Math 121 student who hasn't seen the project yet. Your solution should be organized and have enough detail so that the reader can easily follow it.

1). 10 points) At a foam corn head factory, let C(u) give the cost (in dollars) of producing u pounds of corn heads and let q(t) give the total amount in pounds the factory has produced at time t (measured in days since the beginning of the year.)

(a) What does q(51) = 2000 mean in the context of the problem? (Remember to include units for both input and output!)

2). (b) What does C(2000) = 450 mean in the context of the problem? (Remember to include units for both input and output!)

3). (c) Let F(t) be the composite function F(t) = C(q(t)). Find F(51). What does this tell you about the factory? (Remember to include units for both input and output!)

4). (d) What does q 0 (t) tell you about the factory? Include units.

5. (e) What does C 0 (u) tell you about the factory? Include units.

6. (f) What does F 0 (t) tell you about the factory? Include units.

7. (g) Suppose that q(51) = 2000 and C(51) = 26.5. Which of the following gives a correct formula for F 0 (51)? C 0 (51) q 0 (51) C 0 (2000) q 0 (51) C 0 (51) q 0 (26.5) Explain your choice