SQQM1023 MANAGERIAL MATHEMATICS GROUP ASSIGNMENT 1, SECOND SEMESTER, 2016/2017 SESSION Instructions: i) This is a group assignment consists of 4-5 members. ii) Solve ALL questions in Part A and Part B. iii) Submit by the 8th WEEK (9th - 13th April 2017). PART A 1) Given the function, 2x 2 1 f ( x) x 1 . (6M) (a) name the type of the function (b) f (- 3) (c) f (x - 1 ) (d) domain for the function. 2) Based on the graph below, find: f(x) 10 8 6 4 2 0 (a) 2 f (0) (c) domain 4 6 x (b) f ( 2) (d) range 1 (4M) 3) Find an equation of the line perpendicular to y=3 x5 and passing through (3, 4). (3M) 4) Suppose the demand per week for a product is 100 units when the price is RM 58 per unit and 200 units at RM 51 each. Determine the demand equation if it is linear. (3M) 5) Below are a supply equation and a demand equation for a product. If p represents price per unit in RM and q represents the quantity, 3q - 200p + 1800 = 0 3q + 100p - 1800 = 0 Identify the supply function and the demand function. Give your reason. 6) (4M) Given a profit function for a company is 50q - 450 and the total cost for a product is 25q + 600. (4M) a) Determine the total revenue function. b) Find the break-even point. 7) The total cost to produce an electrical product is C(x) = 350 + 1500x and the total revenue is R(x) = 1560x - x2. Find the maximum profit. (4M) The demand function for a product is given by q2+ 2p = 1600 and the supply function 8) is given by 200 - q2 + 2p = 0. Find: a) equilibrium quantity b) equilibrium price. (3M) (2M) 9) Given log x - log (x - 1) = log 3. Solve for x. (3M) 10) Find the total amount of an investment if you invest RM1000 for 2 years. The bank pays 6% compounded weekly (1 year = 52 weeks). PART B 2 (4M) 1) Let q if 1 q 0 f (q) 3 q if 0 q 3 2q 2 if 3 q 5 Find (a) (c) 1 f ( ) 2 f (3) . (b) . (d) f (0) f (4) . . (e) Domain for the function. 2) Find the slopes, x-intercepts and (5M) y -intercepts of the following lines: (9M) (a) 2 x =53 y . (c) y= ( b ) 3 x407 ( y +1 )=2 . 1 x +8 . 300 3) State whether the following pairs of lines are parallel, perpendicular or neither: (a) y = 5x + 2 and 5x + y - 3 = 0 (c) y = 3 and x = (e) y = 2 5 (b) y = x and y = x 1 3 x + 2 and 5x (d) x + 3y + 5 = 0 and y = 3x 2y = 4 3 (10M) 4) Find the equation of each of the following lines: (8M) (a) The line with slope and passing through the point ( 1, 2). (b) The line passes through the points (4, 8) and (0, -3). (c) x -intercept = and y -intercept = 3 5) Form the straight line equation that has a slope of 3 4 and passes through the point of intersection between y = 3x - 5 and 5x = 1 - 2y. (4M) 6) ABC Company plans to market a new product for RM 18.50 per unit. The variable cost is RM 14 per unit and the fixed cost is RM 2200. Assuming q is the quantity of the product, (a) (b) Find: i) Total cost function. (1M) ii) Profit function. (1M) Determine whether the company will gain profit or loss if 500 units are sold. (3M) 7) Suppose consumers will demand 40 units of a product when the price is RM 12.75 per unit and 25 units when the price is RM 18.75 each. Find the demand equation, assuming that it is linear. Find the price per unit when 37 units are demanded. (4M) 8) Sketch the graph of a quadratic function y = - 2x2 - 16x - 30. (5M) 9) The total cost of a product is C(x) = 1600 + 1500x and its revenue function is represented by R(x) = 1600x - x2. Find the break-even points. (5M) 10) A manufacturer has weekly production cost RM(0.05x - 110) per unit and the fixed cost RM100 000 where x is the number of units produced. Find; (a) The total cost function. (1M) 4 (b) (c) The quantity of product that will minimize the total cost. The minimum cost. (2M) (2M) 11) The demand function is given by p = 0.90 - 0.00045q, where p is the price per unit and q is quantity demanded by consumers. (a) Find the level of production that will maximize the manufacturer's total revenue. (2M) (b) Determine the maximum revenue. (2M) 12) Solve for x. 2 3 (a) (0.001) = 10x (2M) (b) (e5 - 2x) = 1 (2M) (c) ln (4 - x ) + ln 2 = 2 ln x (3M) 13) Given a function to estimate the number of cells after t minutes is f(t) = 2t . Determine how long it would take for the cells to reach 50 000 cells. (3M) 14) On March 20, 1994, RM200 was invested in a fund paying 5% compounded semiannually. How much was in the fund on September 20, 2012? (4M) 15) The current population for Mewah Village is 50 000. The population grows three times after 20 years. Calculate the growth rate per year. (4M) 16) (i) Complete the following table. x -0.5 -0.1 (3M) -0.01 -0.001 0.001 0.01 0.1 0.5 1 (1+ x) x 1 (ii) ( 1+ x ) x =e . From the table, show that lim x 0 5 (2M) 17) Given the function Find lim g(x ) i x ii x lim g(x ) . (2M) . (1M) 6