### Analyzing Fruit Costs and ConsumptionIn this exercise, we analyze the costs and consumption patterns of fruits across two supermarket chains, different types of people, and two towns. The aim is to create matrices solving specific queries about these patterns.#### Data Tables Explanation1. **Cost of Fruit at Two Supermarket Chains** | Fruit | Store A | Store B | |---------|---------|---------| | Apple | $0.10 | $0.15 | | Orange | $0.15 | $0.20 | | Pear | $0.10 | $0.10 | This table represents the price per unit of three types of fruits in two different stores.2. **Amount of Fruit Desired by Two Types of People** | | Apple | Orange | Pear | |---------|-------|--------|------| | Type One| 5 | 10 | 3 | | Type Two| 4 | 5 | 5 | This table shows the quantity of each type of fruit consumed by two categories of people, labelled 'Type One' and 'Type Two'.3. **Population Distribution in Two Towns** | | Type One | Type Two | |---------|----------|----------| | Town X | 1000 | 500 | | Town Y | 2000 | 1000 | This table gives the number of people of each type living in two towns, labeled 'Town X' and 'Town Y'.#### Matrix Solutions1. **Matrix for the Cost of Each Type's Fruit Purchase at Each Store** To determine the total cost per person type at each store, we will multiply the quantity of each fruit type by its corresponding price in each store. **Store A:** \[ \begin{array}{cc} & \text{Type One} & \text{Type Two} \\ \hline \text{Apple} & 5 \times 0.10 & 4 \times 0.10 \\ \text{Orange} & 10 \times 0.15 & 5 \times 0.15 \\ \text{Pear} & 3 \times 0.10 & 5 \times 0.

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Answered: Consider the following tables dealing…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The following table is of profit, revenue, and number of employees of 10 companies. Profit US $ billion Revenue/employee No. of Employees Exxon Royal Dutch British Petroleum Petrofina SA Texao In Elf Aquitaine ENI Chevron Corp. PDVSA SK 11.7 7.4 4.4 2.3 2.9 0.98 3.4 3.1 4.5 0.125 US$ 96,170 74,288 70,859 67,396 92,102 11,461 37,415 84,615 84,821 4,087 a) For the 10 companies, the mean profit per company is $ (Round answer to one decimal place.) c) The "overall" mean profit per employee is $ (Round answer to nearest whole number.) billion US. b) The "overall" mean revenue per employee (i.e., for all employees of these firms combined) of the 10 companies is US. $ (Round answer to nearest whole number.) 122900 105100 56440 69062 29311 83800 80176 39364 56597 30595 US/employee.
B. A manufacturing company is analyzing its accident record. The accidents fall into two categories: ➤Minor-dealt with by first aider: Average cost k50 Major-hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,400, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,600. Manufacturing costs are $14 for each 4-cylinder connecting rod and $19 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5,000 6-cylinder connecting rods and 7,000 4-cylinder connecting rods. Let 56 = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise (a) Using the decision variables x4 and s, write a constraint that limits next…
2. You manage a company that purchases movie theaters. You have a spending goal of $4, 300 million for the purchase of new theaters to seat a total of 4,980 guests. You are given the following data: ABC theaters seat a total of 330 guests and cost $250 million each, CineMovie theaters seat 270- guests and cost $200 million each, and Movies 'n' Stuff theaters seat 240 guests and cost $250 million each. Your company wants you to buy half as many ABC theaters as the combined total of CineMovie and Movies 'n' Stuff theaters. You are tasked with determining how many of each theater your company should purchase. (a) Define variables and determine the constraints associated with this problem. Use them to set up a system of linear equations that models this scenario. (b) After applying Gauss-Jordan reduction, you arrive at the following augmented matrix: T10 0 6 Io 104 0 018 How many of each theater should your company purchase?
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,500, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,900. Manufacturing costs are $13 for each 4-cylinder connecting rod and $16 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If a production changeover is necessary from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 6,000 6-cylinder connecting rods and 8,000 4-cylinder connecting rods. Let x4 = the number of 4-cylinder connecting rods produced next week x6 = the number of 6-cylinder connecting rods produced next week s4 = 1 if the production line is set up to…
A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Labor-Hours per Ski Maximum Labor-Hours Available per Day Department Fabricating Finishing Answer parts (A), (B), and (C) below. Trick Ski 6 1 Slalom Ski 4 1 (A) If the profit on a trick ski is $30 and the profit on a slalom ski is $40, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? The maximum profit is $ The maximum occurs when trick skis and 216 42 slalom skis are produced.
B. A manufacturing company is analyzing its accident record. The accidents fall into two categories: ➤Minor-dealt with by first aider: Average cost k50 Major-hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
A national restaurant chain is composed of 6500 restaurants, each of which is located in close proximity to an interstate highway. The restaurant's business strategy is to serve its core customer base: people travelling on the interstate highway system who are looking for a quality dining experience. Customers generally enjoy the restaurant chain's menu, atmosphere, and consistency from restaurant to restaurant. The company's leadership, located at corporate headquarters, is very interested in the relationship between the cost of a gallon of gasoline and the company's revenue. Specifically, the company is concerned that if gasoline prices rise in the near future, the company's revenue will decline dramatically. The company's research department recently collected data for analysis in order to support leadership's upcoming discussion of whether the company should expand and diversify to locations away from an interstate highway. Annual revenue figures from a random sample…
4. Gabe's Gadgets has stores in three locations, Flint, Pontiac, and Detroit. The number of Gadgets sold in each location in September and October is given in the following table. Flint Pontiac Detroit Flint Pontiac Detroit September 30,000 45,000 70,000 The total cost, in dollars, at each location in September and October is given in the following table. The selling price of each gadget is $30. October 25,000 42,000 60,000 September 8,000 10,000 16,000 October 4,000 9,000 15,000 a. Write a 3x2 matrix X representing the number of gadgets sold at each location in September and October, and a 3x2 matrix C representing the total cost at each location in September and October. b. Find the matrix R where R=30X and explain the meaning of the entry 12. c. Find the matrix P where P=R-C and explain the meaning of the entry P31 -
Problem #3 ( 25 pts). Make sure you show your work. Not just answers or you lose 25 pts). A supermarket employs cashiers, delivery personnel, stock clerks, security personnel, and deli personnel. The distribution of employees according to marital status is shown in the following table: Marital Status Cashiers Stock Delivery Security Deli Total Clerks (T) Personnel (E) Personnel (N) Personnel (1) Married (M) 8 12 11 3 2 36 Single (S) 6 20 3 2 3 34 Divorced (D) 5 5 4 19 19 37 18 6 9 89 If an employee is selected at random, find these probabilities: a) The employee is a stock clerk or married. b) The employee is a stock clerk given that she/he is married.

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