SQQM1023 MANAGERIAL MATHEMATICS GROUP ASSIGNMENT 2 SECOND SEMESTER, 2016/2017 SESSION Instructions: 1. This is a group assignment consisting of 3 to 5 members. 2. Solve ALL questions in Part A and Part B. 3. Submit by the 13th WEEK (14 - 18 May 2017). 4. This assignment contributes to 15% of your coursework, of which 13% is graded on your answers while the remaining 2% is graded on your teamwork. No . Matric No. Question number Name Questions Marks CLO2 Part A 50 CLO3 Part B 15 Total marks 65 Student's mark PART A (50 MARKS) 1. Use the first principle differentiation method to find the first derivative of the function (5 marks) f ( x ) x 4. 2 2. Given x 1 3 x 1 6 y 3. Given the function 4. Given the function . Show that f ( x ) ln x dy 3 x 1 4 dx x 1 . Find x if 5 . 2 f ( x) 27 z f ( x, y ) x3 y 3 3 xy (5 marks) . (5 marks) . a) Find all the critical points. (8 marks) b) Classify each of the critical points. (7 marks) 5. Integrate the following by using the appropriate techniques: e a) ( x +1 2 e )dx x2 (3 marks) 2 8 y e2 y +3 ( ) dy b) (5 marks) 3 4 x 6 x 2 ()dx c) 1 0 (4 marks) 2 x +x x d) ()dx (3 marks) 6. Determine the area of the region bounded by 2 x= y +10, and 2 y . x = (5 marks) PART B (15 MARKS) 1. A manufacturer's production is modeled by the Cobb-Douglas function 3 1 f x, y 100 x 4 y 4 where x represents the units of labor and y represents the units of capital. Each labor unit costs RM200 and each capital unit costs RM250. The total expenses for labor and capital cannot exceed RM50,000. Find the maximum production level. (10 marks) 2. The marginal cost (MC) of a product is given to be a constant multiple of number of units (x) produced. Find the total cost function, if fixed cost is RM5,000 and the cost of producing 50 units is RM5,625