Tutorial letter 101/3/2018 Quantitative Modelling 1 DSC1520 Semesters 1 and 2

Question 1 Find the slope of the line represented by the equation 0 = 6 + 3x − 2y. [1] 2 3 [2] 3 2 [3] 3 [4] 2 [5] None of the above. Question 2 Consider the demand function P = 100 − 5Q, with P being price and Q quantity. Find the price elasticity of demand when Q = 8. Is demand elastic or inelastic? Justify your answer. [1] εd = −1,5; demand is elastic; εd < −1 [2] εd = −0,03; demand is inelastic; |εd| < 1 [3] εd = −1,5; demand is elastic; |εd| > 0 [4] εd = 1,5; demand is inelastic; εd > 1 [5] None of the above. 9 Question 3 Given the demand function P = 60 − 0,2Q. What is the arc price elasticity of demand when price decreases from R50 to R40? [1] −1 3 [2] 1 3 [3] −3 [4] 3 [5] None of the above. Question 4 In the following market: Demand function : Q = 50 − 0,1P Supply function : Q = −10 + 0,1P where P and Q are the price and quantity respectively. Calculate the equilibrium price and quantity. [1] P = 300; Q = 20 [2] P = 200; Q = 30 [3] P = 20; Q = 300 [4] P = 30; Q = 200 [5] None of the above. Question 5 Determine the value of x that solves the inequality: −3(x + 1) + 6  x + 1 3  ≤ 4  x − 1 2  . [1] x ≤ −3 7 [2] x ≤ −1 [3] x ≥ 1 [4] x ≤ 1 [5] None of the above. 10 DSC1520/101/3 Question 6 The linear function 2P = 20 − Q can be graphically represented as: [1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] N o n e o f t h e a b o v e . 11 Question 7 Workers at a building site have the option to eat lunch provided by an outside company. When the price per lunch is R40, there is a demand for 80 lunches. It is known that for each R5 increase in price, demand decreases by three lunches. Determine the demand function for lunches with quantity demanded (Q) as a function of price (P). [1] Q = 104 − 0,6P [2] Q = 136,67 − 1,67P [3] Q = 56 + 0,6P [4] Q = 40 − 3 5 P [5] None of the above. Questions 8 and 9 are based on the following information: The demand and supply functions for accommodation at a B & B are given by Pd = 952 − 8Q and Ps = 400 + 4Q, where P is the price per room and Q is the number of rooms occupied. The following graph represents these functions: B A P D Q C Question 8 The coordinates of the intercepts at A, B and C are [1] A = (0; 95,2), B = (0; 40), C = (11,9; 0). [2] A = (0; 100), B = (0; 119), C = (952; 0). [3] A = (0; 119), B = (0; 100), C = (400; 0). [4] A = (0; 952), B = (0; 400), C = (119; 0). [5] none of the above.