(Bass Diffusion for iPeel) Banana Computer Co. plans to launch its latest consumer electronic...

Question

(Bass Diffusion for iPeel) Banana Computer Co. plans to launch its latest consumer electronic device, the iPeel, early next year. Based on market research, it estimates that the market potential for the iPeel is 170,000 units, with coefficients of innovation and imitation of 0.07 and 0.31, respectively. a) If the iPeel is introduced on January 1, on what date will the sales peak? What will be the demand rate on that date, and how many units will have been sold? b) On what date will 90% of the sales have occurred? c) Plot the demand rate and cumulative demand as a function of time

Komalavalli · Accepted Answer

Bass diffusion model:
1.a)
p- The coefficient of innovation-0.07
q- The coefficient of imitation-0.31
peak sales time t*=ln(q)-ln(p)/p+q
t*=-0.51+1.15/(0.07+0.31)
t*=0.64/0.38
t* = 1.64 years
The time taken to reach peak sales is 1 year 7 month 2 week and 6 days.
m- market potential 1,70,000 units
Sales at time t 
S(t) = m*((p+q)2/p)*e-(p+q)t/(1+q/p*e-(p+q)t)2
S(t) = 170000*((0.07+0.31)2/0.07)*e-(0.07+0.31)1.64/(1+0.31/0.07*e-(0.07+0.31)1.64)2
S(t) = 170000*((0.38)2/0.07)*e-(0.38)1.64/(1+4.43*e-(0.38)1.64)2
S(t) = 170000*((0.144/0.07)*2.1/(1+4.43*2.1)2
S(t) = 170000*((2.05)*2.1/(10.3)2
S(t) =348500*(2.1/(106.09))
S(t) =348500*(0.0197)
S(t)= 6865 units
Demand rate p+(m/q)*t
0.07+(170000/0.31)*1.64 = 548387 units of ipeel
At the time 1.64 year demand is 548387 units of ipeel and sales is 6865 units.
b)
90% of sales occurs at june 1 2023.

(Bass Diffusion for iPeel) Banana Computer Co. plans to launch its latest consumer electronic device, the iPeel, early next year. Based on market research, it estimates that the market potential for...

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