1. An event promoter in Antigua is selling tickets to her all-inclusive Carnivalfete for $150.00 each. She has rented a venue at a cost of $3500, and will incurother fixed costs for a DJ ($1000), MC ($500), stage ($3,000), event staff($4,000), insurance ($500), and marketing ($2,500). The variable costsinclude drinks ($30 per person), and food ($45 per person).a) What is the revenue function for the event? (5 marks)b) What is the costfunction for the event? (5 marks)c) Calculate how many tickets need to be sold in order for the event tobreak even. (5 marks)d) If the promoter, sells 500 tickets:i. Calculate the revenue (2 marks)ii. Calculate the cost(2 marks)iii. Calculate the profit (1 mark)2. The price-demand equation and the costfunction for the production ofhoney is given, respectively, byx = 5,000 - 100p and C(x) = 2,500 + 4x+ 0.01xwhere x is the number of bottles that can be sold at a price of $p perbottle and C(x) is the total cost (in dollars) of producing x bottles.a) Express the price p as a function of the demand x, and find the domain ofthis function. (2 marks)b) Find the marginal cost. (3 marks)c) Find the revenue function and state its domain. (3 marks)d) Find the marginal revenue. (3 marks)e) Find R?(2,000) and R?(3,000) and interpret these quantities. (2 marks)f) Find the profit function in terms of x. (2 marks)g) Find the marginal profit. (3 marks)h) Find P?(1,000) and P?(1,500) and interpret these quantities. (2 marks)3. Given the price-demand equation p + 0.02x = 300a) Express the demand x as a function of the price p. (1 mark)b) Find the elasticity of demand, E(p)*. (7 marks)c) What is the elasticity of demand when p = $100? If this price is decreasedby5%, what is the approximate change in demand? (4 marks)d) What is the elasticity of demand when p = $200? If this price is decreasedby5%, what is the approximate change in demand? (4 marks)e) What is the elasticity of demand when p = $150? If this price is decreasedby 5%, what is the approximate change in demand? (4 marks)4. A vendor makes and sells x strings of beads at her souvenir store everymonth. The monthly cost and price-demand equations are, respectively,C(x) = 0.00002x + 0.04x + 150x + 45000x = 4000 - 200pa) Given the information abovei. How many sets of beadsshould she manufacture each month tomaximize her revenue? (3 marks)ii. What is the maximum monthly revenue? (3 marks)iii. How much should she charge for each set of beads to achievemaximum revenue? (2 mark)b) Given the information abovei. How many sets of beads should she manufacture each month tomaximize her profit? (6 marks)ii. What is the maximum monthly profit? (4 marks)iii. How much should the company charge for each set of beads toachievemaximum profit? (2 mark)5. Find the derivative of:a) f(x) = x? ln x c) y = (3x + 1)?(5 marks)d) Use implicit differentiation to find y?:x + y = 4 (5 marks)

5. Find the derivative of: a) f(x) = x5 In x (5 marks) 4x3 -7x b) f ( x) = (5 marks) 5x2+ 2 c) y = (3x + 1)4 (5 marks) d) Use implicit differentiation to find y': x'+ y = 4