A tech company produces two types of gadgets: SmartWatches and FitnessBands. They aim to maximize their weekly profit considering the availability of components and production capacity.

SmartWatch sells for a profit of $$40$ each, and FitnessBand for $$20$ each. There are two key components in producing their gadgets: microchips and sensors$.$ Each SmartWatch requires $3$ microchips and $2$ sensors$,$ while each FitnessBand requires $1$ microchip and $3$ sensors$.$ The company has $400$ microchips and $600$ sensors available per week. Also, the company wants to ensure that at least $50\%$ of the total gadgets are SmartWatches due to their popularity.Formulate the problem as a linear program.