An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 23-0.2x (for 0 ≤ x ≤ 115), the price function for cars sold in Europe is q = 11 -0.1y (for 0 ≤ y ≤ 110), and the price function for cars sold in Asia is r = 14 -0.1z (for 0 ≤z ≤ 140), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 27 + 9(x+y+z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and P₂ equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia cars cars cars

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 23-0.2x (for 0 ≤ x ≤ 115), the price function for cars sold in Europe is q = 11 -0.1y (for 0 ≤ y ≤ 110), and the price function for cars sold in Asia is r = 14 -0.1z (for 0 ≤z ≤ 140), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 27 + 9(x+y+z) thousand dollars. (a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.] P(x, y, z) = (b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and P₂ equal to zero and solve. Assuming that the maximum exists, it must occur at this point.] America Europe Asia cars cars cars

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Hayfever Farms is an 80‑acre hay farm in Colorado. Due to the legalization of marijuana production in the state, the owners are considering changing the farm's name to Blissful Acres and growing marijuana instead of hay. Use the information presented in the table to answer three questions. Number of acres MC $ MR $ (hay) MR $ (marijuana) 10 320 730 5,600 20 200 730 5,600 30 540 730 5,600 40 730 730 5,600 50 1,200 730 5,600 60 3,200 730 5,600 70 5,600 730 5,600 80 6,700 730 5,600 If they continue to grow only hay, how many acres should Hayfever Farms devote to growing hay in order to maximize profits? area devoted to hay:_______ acres If the owners decide to only grow marijuana, how many acres should Blissful Acres devote to growing marijuana in order to maximize profits? area devoted to marijuana:_______ acres Which outcome likely happens due to the legalization of marijuana production and consumption? The number of growers…
Hanna, who is a 5-year-old girl, eats nothing but pasta, yogurt, and lemonade. Each month her parents buy 32 pounds of pasta, 79 packages of yogurt, and 22 bottles of lemonade. Hanna's parents have recorded the prices per unit of pasta, yogurt, and lemonade for the last four months, as shown in the table below. Hanna's Meals Month Pasta (dollars per pound) Yogurt (dollars per package) Lemonade (dollars per bottle) January $1.83 $1.14 $2.58 February 1.90 1.04 2.35 March 2.07 0.95 2.54 April 2.26 1.04 2.77 Instructions: Round your answers to two decimal places. a. Compute the total monthly cost of Hanna's meals and indicate whether inflation, deflation (negative inflation), or no inflation occurred during these months. In January, the total monthly cost was $. In February, the total monthly cost was $ and (Click to select). In March, the total monthly cost was $ and (Click to select). In April, the total monthly cost was $ and (Click to select). b. If Hanna's parents want to buy the same…
Greenhouse gases trap heat and make the planet warmer. Human activities are responsible for almost all of the increase in greenhouse gases in the atmosphere over the last 150 years. In this part, you will draw two pie graphs. A pie graph is used to show how a certain quantity has been divided into several parts, as well as to show the comparisons among these parts. 1. The data table below shows the total U.S. greenhouse gas emissions by economic sector in 2013, in million metric tons of CO2. On the pie graph provided, complete the graph to show the percent of greenhouse gas emissions for each economic sector. Label each section of the pie graph with its economic sector. The percent for "Agriculture" has been drawn and labeled for you. Economic Sector Electricity Transportation Industry Commercial & Residential Agriculture Percent of Greenhouse Gas Emissions 31 27 21 12 9 80 75 70- 85 65 95 90 wlad Percent 0 100 Agri- culture 55 50 45 10 40 35 20 25 30
A merchant who sells newspapers and magazines at the corner kiosk heard you manage the Times’ inventory and asks for your advice. She has a small, variable number of customers who daily purchase the Chicago Sun Times. In order to get the newspapers in time, she has to place an order for the next day’s newspapers before noon. She pays $0.50 for each newspaper and sells them for $1.50 each. She has kept detailed records of her past sales of the Chicago Sun Times and estimates that 10% of the time she sells 10 newspapers, 40% of the time she sells 11, 30% of the time she sells 12, and 20% of the time she sells 13. (a) What is the merchant’s marginal profit and marginal loss? (b) Determine how many Chicago Sun Times newspapers she should buy every day to maximize expected profits. (c) Calculate the merchant’s expected profits for the optimal order quantity. (d) The merchant has always purchased 13 newspapers, thinking that the best way to maximize profits was to always meet the demand.…
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