A heat pump that operates on a Carnot cycle must deliver thermal energy to your house at a rate of \(12.5 \mathrm{~kW}\) to keep the rooms at \(22^{\circ} \mathrm{C}\). The pump uses outside air at \(-10^{\circ} \mathrm{C}\) as its low-temperature reservoir and runs on electricity that costs \(2.69 \phi / \mathrm{MJ}\). How much does it cost to keep your house at \(22^{\circ} \mathrm{C}\) from 8 a.m. to 10 p.m.?