Math 106--Calculus II: Project 1, Fall 1999

The spagapolis pasta sauce.....

by Gavin LaRose (, Nebraska Wesleyan University, August 1999

©1999 Gavin LaRose (
permission granted to use and distribute free in an academic setting.

PostScript version of project

EcoSystems, Inc.

1 EcoSystem Dr.
Leseatt, TG 71986

30 August 1999

Sophisticated Technical Contractors (STC), Inc.
Suite 1, Strawmarket Business Plaza
Lonlinc, SK 04685

Dear STC:

As you undoubtedly know, EcoSystems (Inc.) is a thriving company founded to bring ecologically sound farm-raised fish to the scenic Leseatt area of Tonwashing in our bright blue environmentally friendly delivery vans. Building on the success of this effort, we have developed a number of fish-farms in the midwest dedicated to the goal of providing fresh, succulent fish to that part of the country, and are now investigating the possibility of expanding our farming beyond fish. In particular, we have come across some data gathered by the great-great grandfather of our company's CEO, the renowned biologist Charles ``Harvey'' Dawson who toured islands in the eastern Pacific during the 1800s in his boat, the H.M.S. Weevil, making observations of wildlife. This data suggests that the addition of turtle production to our farms, allowing the creation of a line of ``Spagapolis Tortoise Pasta Sauce,'' would be to our advantage.

The data collected by Harvey includes information on the productivity of a tortoise (in terms of young produced per year) as a function of the tortoise's age. This is clearly of interest to us as farmers, as we are concerned with maximizing the productivity of the farm. Harvey's data is reproduced in table 1 below. From this data, we are concerned with determining several things. We suspect that if we have a group of breeding tortoises that are producing young for `harvesting' there will be an optimum age at which we should get rid of an existing breeding group and start with a new one, and are interested in determining this age. Preliminary conversations with the inimitable Dr. we-think-the-P.-stands-for-Peerless Gavin LaRose have led us to believe that this will be related to the determination of the total number of young tortoises produced by a tortoise in the breeding group and the average yearly tortoise production for such a member of the group.

Age: 0 2 5 10 15 20 30 40 50
# Young/year: 0 0 4 14 16 23 25 26 17
Table 1: Tortoise productivity as a function of age.

We look forward to receiving your 3--5 page report documenting your solution to this problem on the 13th of September. We have arranged with the aforementioned inimitable Dr. LaRose that he respond to any questions arising as you work on the project. To take advantage of this, however, your group must have made initial contact with him by the 2nd of September to present your initial estimation of what the problem entails. He has also indicated that he will not answer substantial questions on the project solutions over the weekend of the 11th.

Yours most sincerely,
"Chuck" R.D. Arwin
President, EcoSystems, Inc.


Gavin's Calc II Project 1, Fall 1999
Last Modified: Sun Aug 29 17:26:06 CDT 1999
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