What is the total space required for a new factory after 5 years if forecast demand starts at 1200 units and grows by 20% annually, considering machine and support area requirements?

To determine the total space required for a new factory after 5 years, we first need to calculate the demand for the units produced, then figure out how that translates into the required factory space.

The initial demand is 1200 units, and it grows by 20% annually. The formula to calculate the demand for a given year with a growth percentage is:

[ \text{Demand}{n} = \text{Demand}{0} \times (1 + r)^n ]

where:

• (\text{Demand}_{n}) is the demand in year n,

• (\text{Demand}_{0}) is the initial demand,

• (r) is the growth rate (20% = 0.20),

• (n) is the number of years.

Let's calculate the demand for each of the 5 years:

• Year 1: ( 1200 \times (1 + 0.20)^1 = 1200 \times 1.20 = 1440 )

• Year 2: ( 1200 \times (1 + 0.20)^2 = 1200 \times 1.44 = 1728 )

• Year