The number of units N of a finished product produced by a particular automobile company where x units of labor and y units of capital are used is approximated by N=50x^{frac{1}{2}}y^{frac{1}{2}} Estimate how many units will be produced using 256 units of labour and 144 units of capital.

Question
Equations and inequalities
asked 2021-01-31
The number of units N of a finished product produced by a particular automobile company where x units of labor and y units of capital are used is approximated by \(\displaystyle{N}={50}{x}^{{{\frac{{{1}}}{{{2}}}}}}{y}^{{{\frac{{{1}}}{{{2}}}}}}\)
Estimate how many units will be produced using 256 units of labour and 144 units of capital.

Answers (1)

2021-02-01
Substitute x=256 and y=144:
\(\displaystyle{N}={50}{\left({256}\right)}^{{{\frac{{{1}}}{{{2}}}}}}{\left({144}\right)}^{{\frac{{{1}}}{{{2}}}}}\)
Since a^\frac{1}{2} =sqrta, then:
\(\displaystyle{N}={50}\times\sqrt{{256}}​\times\sqrt{{144}}\)
\(\displaystyle{N}={9600}{u}{n}{i}{t}{s}\)
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