Question

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f(m) = (m + 4)2 + 100, and the capacity of machine 2 is defined by the function g(m) = (m + 12)2 − 50, where m is the number of minutes the packaging machine operates. Create the function C(m) that represents the combined capacity of the two machines.

Answer 1

Total capacity = sum of the individual production capacities.

Here,

Total capacity = sum of f(m) = (m + 4)^2 + 100 and g(m) = (m + 12)^2 − 50.

Then f(m) + g(m) = (m + 4)^2 + 100 + (m + 12)^2 − 50.

We must expand the binomial squares in order to combine like terms:

m^2 + 8 m + 16 + 100

+m^2 + 24m + 144 - 50

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Then f(m) + g(m) = 2m^2 + 32m + 160 + 50

f(m) + g(m) = 2m^2 + 32m + 210, where m is the number of

minutes during which the two machines operate.