Management Calculus MATH.1220-031 online Exam 2 M. Stick Spring 2017 All analytic work must be shown. Answers without work are not acceptable. Student name printed:__________________________________________________ Student signature required: All work on this exam was done independently without any sort of collaboration. Student signature:________________________________ 1. (15 pts) Cost is 2.4x+1000, price is 7.2 - 0.001x. Find the best price to maximize the profit. Also graph the profit function and indicate the maximum (x,y) coordinates on your graph. 1 2. Revenue R = x 3 + 6 x 2 , 0 x 25 . 5 a) (7 pts) Find the (x, y) coordinates of the point of inflection (point of diminishing return). Over what interval is the revenue concave up and where is it concave down? b) (8 pts) Find the absolute max and absolute min of the revenue. Show all work. Over what interval is the revenue increasing and where is it decreasing? 3. A rectangular plot is bounded on four sides by fencing. With 160 feet of fencing at your disposal, the goal is to find the largest area that can be enclosed. a) (5 pts) Define the constraint equation and objective function. b) (10 pts) What are the length of the sides of the rectangular plot? Also, what is the maximum area? Show all work. 4. 8000 tickets are sold when the price is $25 per ticket. When the price is $30, 7500 tickets are sold. Everyone at the event spends $5 on concessions. a) (8 pts) Find the linear price equation for tickets and set up a table of (x,y) values showing your work. Note: Let x represent tickets and y represent price. b) (7 pts) Find the best price to maximize the total revenue. 5. (5 pts) Differentiate implicitly to find of the curve at (2,3). dy for xy 2 2 x 3 + y = 5 and then find the slope dx x6 . Find all vertical and horizontal asymptotes. Show all work. x2 4 Also graph the function and indicate the asymptotes on your graph. 6. (10 pts) f ( x) = 1 + 5 x 2 . Currently x=10 items and it increases to 20 items. x a) (4 pts) Evaluate the actual change in the average cost C . 7. Average cost C = 10 b) (4 pts) Evaluate the differential dC (which is an approximation to the actual change) c) (2 pts) Why are C and dC not very close in value and what adjustment might make them closer in value? 8. (5 pts) Revenue R= ( x) 120 x 0.3 x 2 and cost C (= x) 500 + 25 x . Find the rate of dx change in profit with respect to time when x=10 and = 2 units per day. Show all dt work. 9. The demand D( x= ) 75 0.5 x . a) (3 pts) Find the elasticity. b) (3 pts) Evaluate the elasticity at the price x=$40 and state with reason whether the demand is elastic or inelastic. c) (4 pts) Find the value of x for which the revenue is a maximum and at what prices is the elasticity of demand inelastic