The manager of the Frozen Air Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refrigerators and on Tuesday it cost $30,000 to build 40 refrigerators. Find a linear cost function based on this information. 1. What is the daily fixed cost, and what is the marginal cost? 2. Find the price of 13 refrigerators. 2. Linear Demand and Supply Functions from Data You run a small supermarket, and must determine how much to charge for Hot?n?Spicy brand baked beans. The following chart shows weekly sales figures (the demand) for Hot?n?Spicy at two different prices, as well as the number of cans per week that you are prepared to place on sale (the supply) at these prices. 1. Model these data with linear demand and supply functions. Spring: 2023 MATH 163 Page 2 of 3 Price/ Can $0.50 $0.75 Demand (cans sold /week) 400 350 Supply (cans placed on sale/week) 300 500 Table 1: Linear Demand and Supply Functions from Data 2. How do we interpret the slope and qd intercept of the demand equation? 3. How do we interpret the slope of the supply equation qs? 4. Find the equilibrium price and graph demand and supply on the same set of axes. What happens if you charge more than the equilibrium price? 3. Modeling Change Over Time: Growth of Sales The worldwide market for portable navigation devices was expected to grow from 50 million units in 2007 to around 530 million units in 2015. 1. Use this information to model annual worldwide sales of portable navigation devices as a linear function of time t in years since 2007. What is the significance of the slope? t=0, t=8 corresponds to 2007, 2015 respectively 2. Use the model to predict when annual sales of mobile navigation devices will reach 440 million units. 4. Speed/time/Distance (D(t) = at + b B M Two cars A and B are moving in the same direction on a straight line with a speed of VA = 100km/h and VB = 140km/h respectively At time, t = 0s, car A is at O the origin of the coordinate system and car B is at 1 km ahead. 1. Determine the distance traveled by car A and B in term of the time. 2. At what distance and time car B catch up car A. Please go on to the next page... [15] Alt J S 4 1 [10] B i [15] Spring: 2023 MATH 163 Page 3 of 3 5. Body mass and metabolic rate. Metabolic rate The rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. The table below gives data on the lean body mass and resting metabolic rate for 7 men who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person?s weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours, the same calories used to describe the energy content of foods. The researchers believe that lean body mass is an important influence on metabolic rate. Subject Mass x Rate Y 1 62.0 1792 2 62.9 1666 3 48.7 1614 4 51.9 1460 5 51.9 1867 6 62.0 1750 7 49.1 1680 Total x y x2 1. Fill out the table above. 2. By assuming its have a strong linear relationship between Mass (x) and and Rate (y), find the regression line = mx + b with : x = n X 3. Find m = xy-nxy 2 - 2 4. Verify your calculation by using (TI-84) 5. Estimate the Rate (y) when the Mass is (x = 74) 6. Estimate the Mass (x), when the Rate is (y = 1800) y = - Y n b = y=mx= 7. For x = 49.1, find the standard error= [(Predicted values ) -( observed values y)] END [20]