MTH112summer12modelanswer.doc - University of Modern...

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University of Modern Sciences & Arts (MSA) End-Term Examination-Summer 2012 Basic Mathematics For Social Sciences (MTH-112) Model Answer S ECTION (I): T HEORETICAL S TUDY (Total: 15 marks ) (Q1) Answer the following: 1. What is a square matrix? (3 marks) It is a matrix in which number of rows = number of columns 2. What is a row matrix? (2 marks) It is a matrix composed of one row (Q2) Identify which of the following is “True” and which is “False”. 1. A matrix C with dimension 3x1 is a column matrix. (2 marks) True 2. In a linear programming problem, structural constraints are represented by a set of linear inequalities. (2 marks) True 3. In a linear programming problem, the decision variables are the unknowns that have to be either maximized or minimized.(2 marks) False 4. The non-negativity constraints are linear inequalities which state that the decision variables must be always negative. (2 marks) False 5. The following augmented matrix is in reduced form ) 2 ( 3 1 0 5 2 1 marks False S ECTION (II): P ROBLEM S OLVING (Total: 85 marks ) Problem 1: (15 marks) Jane wants to buy a new car which costs $38000. She decided to have a bank loan which is to be repaid in monthly payments with interest charged at the rate of 18 per cent per year compounded monthly. Jane can only afford a monthly payment of $800 and the loan is to be repaid over a 6-year period.
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