Choose a subculture or counterculture(10 points), and using the six elements of culture, research your group and share your research in a PowerPoint presentation.The six elements are: symbols(10 point

ECON 1003 - Graded Tutorial 1 (15 %) Original Deadline for Submission 11 th October 2018 at 8 pm (ECT) Late Submission Deadline 12 th October 201 8 at 8 pm (ECT) (3% deduction) Units: Functions , Equations and Inequalities Submissions typed in WORD and saved in WORD or PDF format are preferred . However, w ritten assignments can be properly scanned , saved and submitted. All submissions must be typed in WORD and saved in the same format. The profit function for a product is given by π(x)= −x3+ 28x2− 57x− 450 , where x is the number of units produced and sold .If break -even occurs when 6 units are produced and sold : i. Find the quadratic factor of π(x). ii. Find a number of units other than 6 that gives break -even for the product . Question 2 (b) A model for the number N of people in a sub -urban community who have heard a certain rumo ur is N = P(1− 1 e0.10d ) where P is the total population of the community and d is the number of days that have elapsed since the rumo ur began .In a community of 2000 residents ,how many days will elapse before 750 have heard the rumo ur?(To the nearest whole number ) (b) The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formula n = ln − ln ln(1− d)where is the salvage value of the machinery , is its initial value ,and d is the annual rate of depreciation . (i) How many years will it take for a piece of machinery to decline in value from $100 ,000 to $10 ,000 if the annual rate of depreciation is (8 % )? (To 1 d.p) (ii) What would the salvage value of the machinery be after 6.5 ye ars ,if its value if the annual rate of depreciation increased to 15% ? (to the nearest hundred ) Question 3 Period Price ($) Quantity Demanded (kgs ) Quantity Supplied (kgs ) Week 1 150 9000 5000 Week 2 400 6000 10000 For the information given in the schedule above ,clearly showing all workings ∶ a. Derive the demand curve (Pd= a+ bQ d). b.Derive the supply curve . (Ps= γ+ δQs) c.Derive the equilibrium price and quantity . Question 4 The price p (in dollars ) and the quantity q sold of boxed lunches obey the demand curve p = 100 − q 3 (i) Find a model that expresses the revenue R as a function of q. (ii) State the domain of R? (iii ) What is the revenue if 120 lunches are sold ? (iv) What quantity q of lunches will max imizes revenue ? What will be the maximum revenue ? (v) What price should the foodseller charge in order to maximize revenue ? Question 5 The car company has found that the revenue from sales of sedans is a function of the unit price p,in dollars ,that it charges .If the revenue R,in dollars ,is R(p)= 1900p − 0.5p2 (i) At what prices p is revenue zero ? (ii) For what range of prices will revenue exceed $1 .2 million ? END OF TUTORIAL