Your client asks you to conduct a pilot study in order to determine the optimum design of a projectile for a new product line. The objective of the pilot study is to design a projectile that will have the greatest accuracy and precision when shot at a target in addition to having the lowest production cost. The client emphasizes that the customers are interested in high performance $($i$.$e$.$ greatest accuracy and precision$)$ projectiles, but cost is still a consideration. In fact, a recent marketing survey conducted by the client indicated that customers have the following tendencies when purchasing projectiles: $10\%$ weight on accuracy, $50\%$ weight on precision, $40\%$ weight on cost$.$ Due to regulatory guidelines, the cylindrical portion of the projectile $($not including the nose cone$)$ must be between $2\mathrm{.}60$ cm and $3\mathrm{.}60$ cm long. Regulatory guidelines also state that test data must include a minimum of $25$ trials in total in order for the results to be valid $($for example, if $5$ projectiles are tested, then a minimum of $5$ test trials per projectile must be conducted for data validity$).$ The density of Alumilite is $1\mathrm{.}05$ g$/$cm$3.$ When a projectile is made during the regular production process, the cost of Alumilite casting resin is $$12\mathrm{.}40/$Liter$,$ however, due to the extensive labor and small batch processing of the prototype projectiles, the prototype cost is $$250\mathrm{.}00/$Liter$.$ It also costs $$200$ per test trial due to setup, equipment, and other material costs. You are given a $$10,000$ budget to conduct the pilot study.