You are the manager of a Midwestern tractor factory planning to produce one of two new products, a zero$-$turn riding lawn mower or a compact tractor. You learned in college that setting the right price for your new product will assist you in maximizing profits while maintaining a good relationship with your customers. You expect the demand for the mower to be $100,000$ units and the demand for the tractor to be $2,000$ units. The annual cost of carrying these products in inventory is $$50$ for a mower and $$100$ for a tractor.