Tutorial5.pdf

UNIVERSITI PUTRA MALAYSIA

FAKULTI SAINS


MTH 3004 PENGENALAN KEPADA MATEMATIK EKONOMI DAN PERNIAGAAN
Tutorial 5
1. Sketch the following quadratic functions:
5x 2
a) f (x) = 5x 2 − 3x +100 b) f (x) = + 75
100
c) f (x) = −x 2 − 5x d) f (x) = −10 + 5x +16x 2

2. A ball is thrown straight up into the air. The height of the ball can be described as a
function of time according to the function h( t )= − 16 t2 + 128 t , where h( t ) is height
measured in meter and t is time measured in seconds.
a) What is the height 2 seconds after the ball is thrown?
b) When will the ball attain its greatest height?
c) When will the ball hit the ground?

3. Determine the equilibrium price and quantity for the product with the given the supply
and demand functions:
2 2
a) ps = q +14q + 22 , pd = −q −10q +150
2 2
b) ps = 2q +10q +10 , pd = −q − 5q + 52
2 2
c) ps = q −100 , pd = q − 40q + 400

4. The demand equation is given by f ( p) =1320 − 4 p where p is stated in RM.
a) Determine the quadratic total revenue.
b) If the price is RM30, what is the total revenue?
c) How many units will be demanded at this price?

5. Consider that the revenue function for pany is given by the equation
R( p) = 350 p −10 p 2
where p represent price in RM.
a) If total expected revenue is RM1000, what is the selling price of the pro