Unformatted text preview: MATH 110 BUSINESS CALCULUS CHAPTER 1 FUNCTIONS AND LINEAR MODELS Section 1.4 Linear Models Applications: 1. COST. A soft‐drink manufacturer can produce 1000 cases of soda in a week at a total cost of $6000, and 1500 cases of soda at a total cost of $8500. Find the manufacturer’s weekly fixed costs and marginal cost per case of soda. 2. BREAK‐EVEN ANALYSIS. The Audubon Society at Enormous State University (ESU) is planning its annual fund‐raising “Eatathon.” The society will charge students 50c/serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at 15c/serving, and the $350 cost of renting the facility for the evening. (a) Write down the associated cost, revenue, and profit functions. (b) How many servings of pasta must the Audubon Society sell in order to break even? (c) What profit (or loss) results from the sales of 1500 servings of pasta? 3. DEMAND FOR CELL PHONES. The following table shows world‐wide sales of Nokia cell phones and their average wholesale prices in 2004: Quarter Second
Wholesale Price ($) 111 Sales (millions) 45.4 Fourth
51.4 (a) Use the data to obtain a linear demand function for Nokia cell phones, and use your demand equation to predict sales if Nokia lowered the price further to $103. (b) Fill in the blanks: For every _________ increase in price, sales of cell phones decrease by _________ units. 4. EQUILIBRIUM PRICE. The demand for your college newspaper is 2000 copies each week if the paper is given away free of charge, and drops to 1000 each week if the charge is 10c/copy. However, the university is prepared to supply only 600 copies per week free of charge, but will supply 1400 each week at 20c per copy. (a) Write down the associated linear demand and supply functions. (b) At what price should the college newspapers be sold so that there is neither a surplus nor a shortage of papers? ...
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- Spring '11
- Calculus, Linear Demand Function, Nokia cell phones, Audubon Society sell, BUSINESS CALCULUS CHAPTER, Audubon Society