01 May Question 1There is no demand for a certain make of pens when the unit pr
Question 1There is no demand for a certain make of pens when the unit price is $12. However, when the unit price is $8, the quantity demanded is 8000 a week. The suppliers will not market any pens if the unit price is $2 or lower. At $4 per pen, however, the manufacturer will make 5000 pens available per week. Both the demand and supply functions are known to be linear.(a) Find the demand equation. (5 marks)(b) Find the supply equation. (5 marks)(c) Find the equilibrium quantity and price. (10 marks)
Question 2Auto-time, a manufacturer of 24-hour variable timers, has a monthly fixed cost of $48,000 and a production cost of $8 for each timer manufactured. The units sell for $14 each.(a) Sketch the graphs of the cost function and the revenue function, and hence find the break-even point graphically. (5 marks)(b) Find the break-even point algebraically. (5 marks)(c) Sketch the graph of the profit function. (5 marks)(d) At what point does the graph of the profit function cross the x-axis? Interpret your result. (5 marks)
Question 3Find how much money should be deposited in a bank paying interest at the rate of 6 percent per year compounded monthly so that at the end of three years the accumulated amount will be $20,000. (10 marks)
Question 4The parents of a child have just come into a large inheritance and wish to establish a trust fund for the child’s college education. If they estimate that they will need $60,000 in 13 years, how much should they set aside in the trust now if they can invest the money at 8.5 percent per year:(a) Compounded annually? (5 marks)(b) Compounded semi-annually? (5 marks)(c) Compounded quarterly? (5 marks)
Question 5A sum of $50,000 is to be repaid over a five-year period through equal instalments made at the end of each year. If an interest of 10 percent per year is charged on the unpaid balance and interest calculations are made at the end of each year.(a) Determine the size of each instalment so that the loan (principal plus interest charges) is
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