Question

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 10 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 7 months (with a standard deviation of 7 months). The average development process lasts 30 months (with a standard deviation of 60 months).

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

The utilization of Mango's development facilities is ___%?

(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.)

The total time is ___ months?

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

Number of years patent life are left for a product is ___ years?

Answer 1

Question: 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 10 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 7 months (with a standard deviation of 7 months). The average development process lasts 30 months (with a standard deviation of 60 months).

Answer:

(a) What is the utilization of Mango’s development facilities?

Utilization is given by:

u = p / (a x m)

Given that;

a = 7 months

p = 30 months

m = 8

Therefore,

u = 30 / (7 x 8)

u = 0.5357 = 0.54 (rounded)

The utilization of Mango's development facilities is 0.54%

(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?

Given that:

CV_a = 7 / 7 = 1

CV_p = 60 / 30 = 2

Waiting time is given by;

T_q = (p / m) x (u^{√2(m+1) -1} / 1 - u) x ( (CV_a² + CV_p² ) / 2 )

T_q = (30/8) x (0.5357^{√2(8+1) -1} / 1-0.5357) x ((1 + 4) / 2)

T_q = (3.75) x ( 0.5357^{√(4.24) -1} / 1 – 0.5357 ) x 2.5

T_q = 3.75 x ( 0.5357^3.243 / 0.4643 ) x 2.5

T_q = 3.75 x 0.285 x 2.5

T_q = 2.667 months

Now,

p = 30 months

T = T_q + p = 2.667 + 30 = 32.667 months = 2.7 years

The total time is 32.66 months (rounded)

(c) How many years of patent life are left for an average product launched by Mango Electronics?

The patent life is given for 10 years.

If the entire development process takes 32.667 months = 2.7 years, then there will be

= 10 - 2.7 = 7.3

Number of years patent life are left for a product is 7.3 years