4 November 1998
Sophisticated and Independent Mathematical Contractors (SIMaC), Inc.
Suite 5, Strawmarket Business Plaza
Lonlinc, SK 04685
Having received your report on the subject of our ``ChipLess'' microchip coating process, it is with considerable faith that we write you again to request your assistance in our work on the marketing of our latest product line expansion. This is to include two new products, which we for the sake of proprietary secrecy shall refer to as ``X'' and ``Y.'' As these are related they share some production costs and resources, resulting in some difficulty in ascertaining the optimum production quantities x and y of each, and it is to determine this best marketing strategy that we are contacting you.
We have found that, appropriately scaled, the production costs of the manufacturing processes for these products is reasonably given by
We also find that the production quantities x and y are constrained by the fact that they share common resources and are influenced by interrelated market forces which, while they are again beyond our control, are more predictable than the material costs noted above. In a series of test marketing efforts we were able to vary the sustainable production of x and y with time, finding that they at maximum production behaved as shown in figure 1 to the right. We believe this to indicate that x and y have some sort of direct relationship that will constrain the production when we commence with our long-term manufacturing and marketing of X and Y.
Insofar as possible we would like your analysis to be applicable for general values of a and b, though we do expect that a will be approximately 1 and b approximately 2.
We look forward to receiving your final report on or before the 30th
of November. To assure your success, we have again arranged for the
most estimable of mathematicians, Dr. P. Gavin LaRose, to answer any
questions you may have in the course of your investigation. Please
note, however, that he will unfortunately be unavailable to
assist with this project over the weekend of the 27th--29th of
November. You should plan on meeting with him before the week of
the 16th of November to verify your initial progress. We have also
made available, through him, a number of sample reports that may prove
useful as you develop your report.
E. Idu Pont
President, Chemproc, Inc.