Page 10 of 11 ZOOM 11. A hotel in South Carolina is able to rent all of its 300 rooms at a rent of $80 per room. For every $1 increase in price, 3 fewer rooms are rented. How much should the hotel rent each room to get the maximum revenue? At this price, how many rooms are rented? 12. Given the following price-demand and cost functions for a product: p(x) = 10 -0.001x C(x) = 5000 + 2x a) Determine the revenue and profit functions.Page 10 of 11 ZOOM + 12. Given the following price-demand and cost functions for a product: p(x) = 10 -0.001x C(x) = 5000 + 2x a) Determine the revenue and profit functions. b) Using calculus determine how many products should be sold to maximize profit? c) What is the maximum profit? d) For maximum profit, what price should the product be sold for? 10Page 11 of 11 - ZOOM 13. A firm produces and sells two types of items each week. X number of type A and Y number of type B. The weekly revenue and cost functions in dollars are R(x, y) = 8 - x + 90y + 0.04xy - 0.05x - 0.05y? C(x, y) = 8x + 6y + 20000 a. Determine the Profit function (Revenue - Cost) b. Find P.(1200,1800) and interpret c. Find P,(1200,1800) and interpret 14. A company has developed the yearly profit equation P(x,y) = -22x2 + 22xy - 1ly? + 110x - 44y -23Page 11 of 11 ZOOM + 14. A company has developed the yearly profit equation P(x,y) = -22x2 + 22xy - 1ly# + 110x - 44y -23 where x is the number in thousands of their standard product and y is the number in thousands of their deluxe product produced and sold per year and P is the profit, in thousands of dollars. a. Find the critical point and show that this is a maximum b. How many of each product should be produced to realize a maximum profit? c. What is the maximum profit? 11