DSC1520 - Quantitative Modelling I ASSIGNMENT.

DSC1520 - Quantitative Modelling I. The daily rate of sales of a product (in units per day) is approximated by the exponential equation S(t) = 1 800 + 1 500e −0,3t+1,5 , with t the number of days it has been on the market. After how many days, rounded to a whole number, will the rate of sale be 2 000 units per day? [1] 4 [2] 7 [3] 11 [4] 12 [5] None of the above. Question 3 If the demand function is P = 80 − 0,5Q where P and Q are the price and quantity respectively, determine the expression for price elasticity of demand in terms of P only. [1] P − 80 P [2] P P − 80 [3] P P − 1 600 [4] 1 600 P − 80 [5] None of the above. DSC1520 Questions 4 and 5 are based on the following information: Consider the market defined by the following demand and supply functions, Pd = 50 − 0,6Q and Ps = 20 + 0,4Q where P and Q are the price and quantity respectively. The following graph represents these functions. P Q Ps Pd Question 4 The coordinates of the intercept are [1] (32; 30). [2] (30; 32). [3] (68; 30). [4] (8; 70). [5] none of the above. Question 5 At the intercept [1] 30 or 32 units are produced to break even [2] equilibrium is reached when 30 units are produced at R32 per unit [3] consumer surplus is 68 and producer surplus is 30 [4] Point elasticity of demand is 8 and arc elasticity of demand is 70 [5] None of the above. 3 Question 6 Consider the market defined by the following demand and supply functions, Pd = 50 − 3Q and Ps = 14 + 1,5Q where P and Q are the price and quantity respectively. The producer and consumer surplus of the product respectively are [1] 8 and 48. [2] 48 and 96. [3] 96 and 8. [4] 192 and 96. [5] none of the above. Question 7 Use rules of logarithms to solve the equation 3 ln(5x) − 2 ln x = 7. [1] 0,11. [2] 8,77. [3] 29,33. [4] 1 096. [5] None of the above. Question 8 The demand function is equal to P = 60 − 2,5Q with P and Q the price and quantity respectively. Determine the expression for the price elasticity of demand if the price is equal to P = 10. Indicate whether the demand is elastic or not. [1] εd = −2,500; elastic [2] εd = −0,008; inelastic [3] εd = −0,200; inelastic [4] εd = −0,200; elastic [5] None of the above. 4 DSC1520 Question 9 The demand and cost functions for a commodity are given by the equations Demand function: Q = 6 000 − 30P Cost function: C(Q) = 5 000 + 2Q, where P and Q are the price and quantity respectively. The total revenue function (TR) and the company’s profit function, in terms of P are [1] T R = 6 000 − 30P; Profit = −90P − 1 000. [2] T R = P(6 000 − 30P 2 ); Profit = −30P 3 + 5 940P − 17 000. [3] T R = 6 000P − 30P 2 ; Profit = − 30P 2 + 6 060P − 17 000. [4] T R = 6 000P + 30P 2 ; − 30P 2 + 6 060P − 7 000. [5] none of the above. Question 10 The demand and supply functions of a product are given by Pd = Q 2 + 2Q + 5 and Ps = 29 − 3Q, where P and Q are the price and quantity respectively. Determine the equilibrium price and quantity