Q$8\mathrm{.}9($Mango Electronics Inc.$)$ Mango Electronics Inc. is a Fortune $500$ company that develops and markets innovative consumer electronics products. The development process pro$-$ ceeds as follows.

Mango researches new technologies to address unmet market needs. Patents are filed for products that have the requisite market potential. Patents are granted for a period of $20$ years starting from the date of issue. After receiving a patent, the patented technologies are developed into marketable products at five independent development centers. Each product is only developed at one center. Each center has all the requisite skills to bring any products to market $($a center works on one product at a time$).$ On average, Mango files a patent every $7$ months $($with a standard deviation of $7$ months$).$ The average development process lasts $28$ months $($with a standard deviation of $56$ months$).$

$1.$What is the utilization of Mango$$s development facilities?

$2.$How long does it take an average technology to go from filing a patent to being launched in the market as a commercial product?

$3.$How many years of patent life are left for an average product launched by Mango Electronics?