You$$ve already completed a preliminary version of this model with your class, the Historic Hotel activity. In the Historic Hotel activity, you considered a hotel in which all $80$ rooms can be rented if the cost for the room is $$60$ for a night. Each time the owner increases the cost by $$1,$ one room will be vacant. In addition to this potential reduction in profit, the owner must pay $$4$ for service and maintenance for each occupied room. Some people might solve the problem by finding the vertex of a parabola that opens downward.

For this five stage model, you are asked to play the role of a $$social entrepreneur$$ and design your own realistic business. A social entrepreneur is a person who creates a business venture that can pay their own bills but also, that addresses a community need. As a social entrepreneur, you can focus on making a fair profit for yourself because you need to make a comfortable living, but you try to do this in a way that benefits other people. Social entrepreneurship critiques the dichotomy of altruism and self$-$interest.

Try to make a simple model of a business at first. It$$s not easy, because you$$ll have to try out several scenarios in order to get numbers that are even slightly realistic. You can use Excel, Google Sheets, Desmos, equations, or calculations with a calculator. You can imagine this business to be a small side business or your primary employment. It could involve you alone or a group of people.

Keep your basic answer simple. For your Extend answer, you can factor in an additional realistic feature. Or$,$ for your Extend answer, you can try to weave together the algebra regarding parabolas, vertices and quadratic equations, and explain how some of this mathematics