)Given that a company can sell as many units of its products as it can manufacture with in a given period of time at ₵18 each. Its fixed cost is known to be ₵240 in addition to its marginal cost ₵14 for each unit produced. (i)Deduce various functions with respect to the company’s cost and revenue at its production levels.
BAHAGIAN A 1 MID TRIMESTER EXAMINATION KCC WEEKEND JANUARY 2022 TRIMESTER DATE: MARCH 2022 COURSE CODE: MATH107 COURSE TITLE: BUSINESS MATHEMATICS AND STATISTICS I LECTURER NAME: MICHAEL ADU BENSON COURSE OUTLINE (MAIN TOPICS) QUESTION NO. MajorTopic-1 Graphs and Functions. 2(a), 2b , 3a MajorTopic-2 Linear Equations 1 1 (c) , 3(b), 4a, 5a MajorTopic-3 Linear Equations 2 1 (a) , 2 (b) , 3(b), 4a, 5a MajorTopic-4 Linear Equations 3 1b, 3b, 4 (a), 5a MajorTopic-5 Quadratic Equations 1 (c) , 2 (a) , 5(c) MajorTopic-6 Matrix Algebra 2 (c), 3c, 4(b) MajorTopic-7 MajorTopic-8 2 PART A [50 MARKS] THREE QUESTIONS ANSWER TWO Question 1 (a) Discuss on the level of output needed for a firm’s total revenue given as $ 600, of which its demand schedule is ? = 70 − ?. Major Topic: 3 Linear Equations 2 Blooms Designation (AN) Score 6 (b) In a competitive market the supply and demand schedule are respectively given as follows; ? = 20 + 2? and ? = 610 − 3?. Comment and interpret on your computed equilibrium price and quantity. Major Topic 4 Linear and Equations 3 Blooms Designation (AP) Score 7 (c) Given that a company can sell as many units of its products as it can manufacture with in a given period of time at ₵18 each. Its fixed cost is known to be ₵240 in addition to its marginal cost ₵14 for each unit produced. (i)Deduce various functions with respect to the company’s cost and revenue at its production levels. Major Topic: 2 &5 Linear Equations 1 / Quadratic Equations Blooms Designation AP/AN Score 5 (ii) As a consultant to the company advice management how much the company need to produce in order to break-even. 3 Major Topic: 2 &5 Linear Equations 1 / Quadratic Equations Blooms Designation AP/AN Score 7 Total [25] Question 2 (a) Consider the given function = 4? − ?2 ; for 0 ≤ ? ≤ 9, plot the graph of the function and comment the nature of this function. Major Topic 1 &5 Graphs and Functions / Quadratic Equations Blooms Designation AN Score 5 (b) (i)Make up your own linear functions for supply and demand schedules; Major Topic 1&3 Graphs and Functions /Linear Equations 2 Blooms Designation AP/AN Score 2 (ii)Compute and comment the values of price and quantity, graphically. Major Topic 1&3 Graphs and Functions /Linear Equations 2 Blooms Designation AP/AN Score 4 4 (iii) Solve your set of linear simultaneous equation algebraically, and compare your answer with the values for (ii) Major Topic 1&3 Graphs and Functions /Linear Equations 2 Blooms Designation AP/AN Score 5 (c) use matrix to solve the following system of equation 3? + 4? = −1 5? − 4? = 9 Major Topic 6 Matrix Algebra Blooms Designation AN Score 9 Total [25] Question 3 (a) Plot the graph of the following functions and comment on the nature of the function, (i) 3? − ? = 4. (ii) 5? + ? = 6 Major Topic 1 Graphs and Functions. Blooms Designation AP Score 6 5 (b) A firm manufactures product ? and can sell any amount at a price ₵25 a unit. The firm has to pay fixed costs of ₵200 plus a marginal cost of ₵20 for each unit produced. (i) How much of ? must be produced to make a profit. Major Topic 2,3,4 Linear Equations 1,2 & 3 Blooms Designation AN/AP Score 5 (ii) If price is cut to ₵24, what happens to the break-even output. Major Topic 2,3,4 Linear Equations 1,2 & 3 Blooms Designation AN/AP Score 7 (c) A firm uses three different inputs A, B and C to make three final products X, Y and Z. Each of unit X produced requires 4 units of A, 6 units of B and 5 units of C. Each of unit Y produced requires 5 units of A, 7 units of B and 4 units of C. Each of unit Z produced requires 3 units of A, 3 units of B and 5 units of C. 6 (i) Set up these inputs requirements in matrix format