Question

the acme corporation believes that the production of its product in its present facilities will assume logistic growth. these facilities limit production to at most 600 units per day. presently 240 units per day are produced. the production will increase to 360 units per day in one year. what is the anticipated daily production 5 years from now

Answer 1

594 units

Step-by-step explanation:

We must apply the logistics growth model, since applying linear or exponential growth will result in numbers which are much higher than the total production capacity of this facility. When we use the logistics growth model, the growth rate decreases as the resource limit approaches.

f(x) = c / (1 + ae⁻ᵇˣ)

initial value = c / (1 + a) = 240

600 = 240 + 240a

360 = 240a

a = 1.5

b = growth rate = (360 - 240) / 240 = 0.5

x = 5

e = 2.71828

f(x) = 600 / [1 + [1.5 x (2.71828⁻⁵) = 600 / 1.010106954 = 593.9965 = 594 units