Mango Electronics Inc. is a Fortune $500$ company that develops and markets innovative consumer electronics products. The

development process proceeds 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 $15$ years starting from the date of issue. After receiving a patent, the patented

technologies are then developed into marketable products at $8$ independent development centers. Each product is only developed at

one center. Each center has all the requisite skills to bring any of the products to market $($a center works on one product at a time$).$ On

average, Mango files a patent every $6$ months $($with a standard deviation of $6$ months$).$ The average development process lasts $20$

months $($with a standard deviation of $40$ months$).$

$($a$)$ What is the utilization of Mango's development facilities? $($Round your answer to two decimal places.$)$

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

$($Round your answer to one decimal places.$)$

$($c$)$ How many years of patent life are left for an average product launched by Mango Electronics? $($Round your answer to one decimal

places.$)$