In $2003,$ Du Pont introduced Arathorn $25,$ a polyethylene resin designed to compete with other resins in the manufacture of flexible pipe. Tests indicated that Alathon $25$ pipe had failure rates of $3\%$ compared with $8\%$ for the competition. Farmers purchased Alathon pipe as part of below$-$ground irrigation system. The common substitute for Alathon pipe was a pipe made of an off$-$grade resin selling for $$6\mathrm{.}5$ per hundred feet. Labor cost of replacing a failed pipe is about $$60.$ Pipe failures, if not detected quickly, can also damage crops. The damage could range from $0($if the plants were mature$)$ to $$40$ when vulnerable seedlings were washed out. Young, poorly rooted crops are in place approximately $20\%$ of the time that the irrigation system is in use.

Required

i$)$ What was the product$’$s economic value for the farmers?

ii$)$ What if the failure rate is reduced from $7\%$ to $1\%($instead of $8\%$ to $3\%)?$