Please help to solve problems 8 through 13 Please show full work! Thanks tutors.

Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following functions where p is the price. S(p) = -340 + 30p D(p) = 1200-40p a. Find the equilibrium price for the T-shirts at this concert. Round your answer to the nearest dollar as needed b. What is the equilibrium quantity? C . Determine the prices for which quantity demanded is greater than quantity supplied. 9. For the quadratic function f(x) = -x2 + 4x -3 a. Find the vertex b. Find the x intercepts if any C . Find the y intercept if any d. Find the axis of symmetry e. Graph the function, please make sure to label your points and make your own scale nicely 10. Determine the quadratic function f whose graph is given. The vertex is (1, -1) and the other given point is (3, 7) 11. Jason has available 200 yards of fencing and wishes to enclose a rectangular area. . Express the area A of the rectangle as a function of the width W of the rectangle. b. For what value of W is the area largest? c. What is the maximum area? 12. Farmer McDonald has 3500 meters of fencing and wants to enclose a rectangular plot that border on a river. If farmer McDonald does not fence the side along the river, what is the largest area 13. The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation that can be enclosed? a. Find a model that expresses the revenue R as a function of p. (Hint: R = xp) X = -9p + 900. b. What is the domain of R? Assume that R is nonnegative C. What price p maximizes revenue? d. What is the maximum revenue? e. How many units are sold at this price