$($Mango Electronics Inc.$)$ 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

$20$ years starting from the date of issue. After receiving a patent, the patented technologies

are then 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 of the products to market $($a center works on one product at a time$).$ On average,

Mango files a patent every $7$ months $($with standard deviation of $7$ months$).$ The average

development process lasts $28$ months $($with standard deviation of $56$ months$).$

a$.$ What is the utilization of Mango$$s development facilities? $[9\mathrm{.}6]$

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? $[9\mathrm{.}6]$

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