A \(30 \mathrm{ft} \times 20 \mathrm{ft}\) office space has a photosensor dimmer control working with installed lighting of \(2 \mathrm{~W} / \mathrm{ft}^{2}\). The required workplace illuminance is \(60 \mathrm{fc}\) and the available daylighting is calculated as \(40 \mathrm{fc}\) on the summer peak afternoon. Determine the payback period for the dimmer control system assuming the following: 1-1/2 ton cooling installed for \(600 \mathrm{ft}^{2}\) at \(\$ 2200 /\) ton, lighting control system cost at \(\$ 1 / \mathrm{ft}^{2}, 30 \%\) reduction in annual lighting due to daylighting, \(\$ 0.10 / \mathrm{kW}\) h electricity cost, and cooling for 6 months at a \(\operatorname{COP}_{c}=2.5\).