2. "All or Nothing" is a logic game. In this game you must choose between the best of three "Popcorn Stand" scenarios. Choose t most promising scenario and win "All" the profits or choose wrong and get "Nothing". Market study shows that for every $0.10 decrease from a $5.00 popcorn bag you will sell 1000 more bags of popcorn. This produces a price function of p(x)=5.000.10x for the number of bags sold " x " in thousands. The revenue function is then: R(x)=x(5.000.10x)R(x)=0.10x2+5.00x Choose the scenario that will give the best profit, P(x)= ? given the three different Costs: Scenario 1C(x)=8.00+2.00x Scenario 2C(x)=9.00+1.50x Scenario 3C(x)=7.00+2.50x A. Graph the equation of your best scenario. B. List the equation for the best scenario using function notation to express your answer. C. i) Identify the input variable? ii) Identify the output variable? iii) Is P(x) a function? State your reasoning. iv) If the profit function is restricted to the domain where: 12.5=x=21.8, what is the range for Scenario 3? D. i) What is the profit function for each scenario? ii) What is the discriminant for each scenario? iii) What is the maximum point for each scenario ( x max, P(x max ) ? iv) What do you think is the best scenario for the owners (give a reason)? v) What do you think is the best scenario for the consumer (give a reason)? vi) Who should have the greatest influence in the decision of costs (give a reason)