Determine the number and roof placement of \(10 \mathrm{ft} \times 4 \mathrm{ft}\) skylights needed for a \(50 \mathrm{ft} \times\) \(50 \mathrm{ft} \times 10 \mathrm{ft}\) high office when the horizontal illuminance is \(6000 \mathrm{fc}\), the skylight has \(45 \%\) net transmittance, and the required workplace illuminance is \(100 \mathrm{fc}\).