MTH105: If the Supply and Demand Equations of a Certain Product are 140𝑞 − 𝑟 − 280 = 0: Fundamentals of Mathematics Assignment, SUSS, Singapore

Assignment Brief:

Problem 1. If the supply and demand equations of a certain product are 140𝑞 − 𝑟 − 280 = 0 and 80𝑞 + 𝑟 − 600 = 0, respectively, find the equilibrium price and quantity.

Problem 2. The demand function for a manufacturer’s product is 𝑞 = 𝑓(𝑟) = 400 − 5𝑟, where 𝑞 is the price per unit when 𝑟 units are demanded.

(a) Find the level of production that maximizes the manufacturer’s total revenue, and determine this revenue.

(b) Sketch the graph of the revenue function.

Problem 3. Find an equation of the straight line passing through the points (−1, −2) and (4, 1).

Problem 4. A savings account pays interest at the rate of 3.5% compounded semiannually. What amount must be deposited now so that $400 can be withdrawn at the end of every six months for the next 20 years?

Problem 5. A savings account contains £200. How much must have been deposited 8 years ago when the account was opened, if no money has been deposited in the account since? Assume an interest rate of 4% compounded annually.

Problem 6. A town with a population of 50,000 in 2020 is growing at a rate of 8% per year. Determine the population 10 years from now if this rate of growth is maintained.

Problem 7. The cost of publication of each copy of a magazine is £1.20. It is sold to dealers for £1.40 a copy. The amount received for advertising is 15% of the amount received for all magazines sold beyond 100,000 copies. Find the least number of magazines that can be published profitably, if 75% of the issues published are sold.