QUESTION ONE A. A manufacturer of a new product has found that he can sell 70 units a week direct to the customer if the price is $48. In error, the price was recently advertised at $78 and, as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to (i) Show the equation of the demand function relating price (p) to quantity demanded (x), assuming it is a straight line, is p = 118 - x 14 Marks] (ii) Find where the manufacturer breaks even; [3 Marks (iii) Find the quantity demanded at an optimal profit level and the profit generated at this level; |3 Marks (iv) Recommend a unit price which would maximize profit. [2 Marks B. Sofia makes an initial deposit of GH1 2000 in a bank account. The deposit is to eam interest annually at the rate of 8% for 4% years. (i) Find how much Sofia will have in the account at the end of the 4% years, if the interest compounds annually. [2 marks] (ii) Suppose the interest compounded quarterly, how much would she have at the end of the 4% years? [2 marks (iii) Make a table showing the growth of the account for the first 4 quarters. (4 marks] Quantitative Methods l_May, 2018 Page 2 QUESTION TWO A. A company produces three different sizes of bottle water classified as large, medium and small. Its production expenses are divided into three categories. In each category, an estimate is given for the cost of producing a bottle water of each size. An estimate is also made of the total costs in the year in each of the categories, raw materials, labour and overheads. These estimates in Ghana cedi (GHC) are reported in the following table. Size of bottle water Expenses Large Medium Small Total Cost (GHC) Raw materials 6 3 2 2390 Labour 8 5 6 4300 Overhead 4 3 2 2008 (1) Set up the system of linear equations which when solved will determine the amount of each size of bottle water produced 11 Marks (ii) By the Cramer's rule, determine the amount of each size of bottle water produced during the year. [13 Marks B. A firm's demand function has been estimated to be P=500- 0.29 Where, represents output (in units). The firm's total cost (TC, in GHC) of production is given by; TC = 2000+509. Find the: marginal profit function 14 marks (ii) marginal profit when output level is 500 units. 12 marks QUESTION THREE A. A company produces two products that are processed on two assembly lines. Assembly line one has 100 available hours and assembly line two has 42 available hours. Each product requires 10 hours of processing time on line one, while on line two product A require 7 hours and product B requires 3 hours. The profit for product A is GHC 6 per unit and the profit for product B is GHC 4 per unit. () Formulate the linear programming model for the above problem. 12 Marks (ii) Draw a graph of the problem and indicate the feasible region. 15 Marks (iii) Find how many of each product should be produced to realize a maximum profit . 15 Marks B. If the investment flow is given by; I(t)=9000/ Calculate the number of years required before the capital stock exceeds $100000. (8marks|