1993 MCM B：The Optimal Composting Problem
An environmentally conscious institutional cafeteria is recycling customers’ uneaten food into compost by means of microorganisms. Each day, the cafeteria blends the leftover food into a slurry, mixes the slurry with crisp salad wastes from the kitchen and a small amount of shredded newspaper, and feeds the resulting mixture to a culture of fungi and soil bacteria, which digest slurry, greens, and paper into usable compost. The crisp greens provide pockets of oxygen for the fungi culture, and the paper absorbs excess humidity. At times, however, the fungi culture appears unable or unwilling to digest as much of the leftovers as customers leave; the cafeteria does not blame the chef for the fungi culture’s lack of appetite. Also, the cafeteria has received offers for the purchase of large quantities of its compost. Therefore, the cafeteria is investigating ways to increase its production of compost. Since it cannot yet afford to build a new composting facility, the cafeteria seeks methods to accelerate the fungi culture’s activity, for instance, by optimizing the fungi culture’s environment (currently held at about 120℉ and 100% humidity), or by optimizing the composition of the mixture fed to the fungi culture, or both.
Determine whether any relation exists between the proportions of slurry, greens, and paper in the mixture fed to the fungi culture, and the rate at which the fungi culture composts the mixture. If no relation exists, state so. Otherwise, determine what proportions would accelerate the fungi culture’s activity.
In addition to the technical report following the format prescribed in the contest instructions, provide a one-page nontechnical recommendation for implementation for the cafeteria manager.
Table 1 shows the composition of various mixtures in pounds of each ingredient kept in separate bins, and the time that it took the fungi culture to compost the mixtures, from the date fed to the date completely composted.