IIIAplctnLnrFnctns

IIIAplctnLnrFnctns - Dr Raja Latif 3.2 Applications and...

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Dr. Raja Latif. 3.2: Applications and Linear Functions. Math 131(043) Pg: 1 SUPPLY AND DEMAND: The curves that show the quantity that will be supplied at a given price and the quantity that will be demanded at a given price are called SUPPLY and DEMAND CURVES. Supply and demand are equal at the point where the supply curve intersects the demand curve. This is the equilibrium point. Its second coordinate is the equilibrium price, the price at which the same quantity will be supplied as is demanded. Its first coordinate is the quantity that will be demanded and supplied at the equilibrium price; this number is called either the equilibrium demand or the equilibrium supply. Customarily, a demand equation (as well as a supply equation) expresses p in terms of q and actually defines a function of q. LINEAR FUNCTION. A function is a linear function if and only if f(x) can be written in the form f(x) ax b, where a and b are constants and a 0. The graph of a linear function is a staright line. We say that the function f(x) ax b has slope a. 140AL4Example.(Demand) A dealer can sell 20 electric shavers per day at \$25 per shaver, but he can sell 30 shavers if he charges \$20 per shaver. Determine the demand equation, assuming it is linear. Solution. Taking the quantity x demanded as the abscissa (or x-coordinate) and the price p per unit as the ordinate (or y-coordinate), the two points on the demand

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Dr. Raja Latif. 3.2: Applications and Linear Functions. Math 131(043) Pg: 2 curve have coordinates x 20, p 25 and x 30, p 20. Thus the points are (20, 25) and (30, 20). Since the demand equation is linear, it is given by the equation of the straight line passing through the two points (20, 25) and (30, 20). The slope of the line joining these two points is m 20 25 30 20 5 10 0.5. From the point-slope formula, the equation of the line through (20, 25) with slope m 0.5 is y y 1 m(x x 1 . Since y p, we have p 25 0.5 (x 20) p 0.5x 35 Which is the required demand equation. p 0.5 x 35 75 62.5 50 37.5 25 12.5 0 30 20 10 0 x p 
Dr. Raja Latif. 3.2: Applications and Linear Functions. Math 131(043) Pg: 3 141AL15. When the price per unit is \$10, the supply will be 80 units per day whereas it will be 90 units at a unit price of \$10.50. Determine the supply equation, assuming it is linear. Draw the supply curve. [Answer p 1 20 x 6.] SOLUTION. Taking the quantity x demanded as the abscissa (or x-coordinate) and the price p per unit as the

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IIIAplctnLnrFnctns - Dr Raja Latif 3.2 Applications and...

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