Math 118 Worksheet 3 Names: (Covers 1.31.7) 1. Find the average rate of change of f (x) = 2x2 between x = 1 and x = 3. Illustrate your answer graphically. 2. A company producing jigsaw puzzles has fixed costs of $6000 and variable costs of $2 per puzzle. The company sells the puzzles for $5 each. a. Find formulas for the cost function, the revenue function, and the profit function. h. Find the marginal cost. c. Sketch the graph of R (q) and C (q) on the same axes. What is the breaking point, qo, for the company? 3. One of the tables below represents a supply curve; the other represents a demand curve. Table 1.28 p($/unit) 182 167 153 143 133 125 118 9 (quantity) 5 10 15 20 25 30 35 Table 1.29 p($/unit) 6 35 66 110 166 235 316 9 (quantity) 5 10 15 20 25 30 0 35 a. Which table represents which curve? b. At a price of $155, approximately how many items would consumers purchase? C. At a price of $155, approximately how many items would manufacturers supply? d. What would the price have to be if you wanted consumers to buy at least 20 items?Maximizing Revenue for Popsicles. a. Which of the equations below could be a realistic demand equation for popsicles at a stand in Venice Beach? Explain your answer below. i. q = 100p + 400 ii. q = 100p + 4-00 iii. None of the above. b. If the demand function is as we decided upon in part a., nd the revenue R(q) as a function of the number of popsicles sold. c. Sketch the graph of the revenue function y = R(q). (Hint: complete the square, or you may use a graphing calculator or computer (such as Desmos) to help you sketch). How many popsicles should be sold in order to maximize revenue? How much should the stand charge for each popsicle in order to maximize their revenue? If the popsicle stand is currently charging $1 per popsicle, will their revenue increase or decrease if they sell one more popsicle? (Hint: look at the graph of the revenue function). How could this be? Shouldn't increasing sales always increase revenue? Explain. Again, just by looking at the graph, estimate MR (200). Explain. 5. A person is working in a company and there are two payment options being offered. Option 1 is to pay $40,000 + 5,000t when this person has worked in this company for t years. Option 2 is to pay $30,000 + 60'2\". a. If this person has worked in this company for only one year, which payment option should they chose? Explain your answer. b. If this person has worked in this company for 50 years, which payment option should they choose? Explain your