A product is made by only two competing companies. Suppose Company X retains two-thirds of its customers and loses one-third to Company Y each year, and Company Y retains three-quarters of its customers and losesone-quarter to Company X each year. We can represent the number of customers each company had last year byDwhere xo is the number Company X had and yo is the number Company Y had. Then the number that each will have this year can be represented by3If Company X has 2900 customers and Company Y has 2500 customers this year, how many customers did each have last year?Company XCompany YNeed Help?Read Itcustomerscustomers

We have to find the value of x0

Answered: A product is made by only two competing…

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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A company manufactures three types of lamps, labeled A, B, and C. Each lamp is processed in two departments, I and II. Total available work-hours per day for departments I and II are 409 and 591, respectively. No additional labor is available. Time requirements and profit per unit for each lamp type are shown in the table to the right. The company has assigned you as the accounting member of its profit planning committee to determine the numbers of types of A, B, and C lamps that it should produce in order to maximize its total profit from the sale of lamps. The following questions relate to a linear programming model that your group has developed. a. What would the coefficients of the objective function be? OA. 2, 3, 1 OB. 409, 591 OC. 8, 7, 6 OD. 4, 2, 3 b. What would the constraints in the model be? OA. 4, 2, 3 OB. 2, 3, 1 OC. 8, 7, 6 OD. 409, 591 c. What could the constraint imposed by the available work-hours in department I be expressed as? OA. 4x₁ + 2x₂ + 3x3 ≤ 409 O B. 2x₁ +…
2. From Wikipedia, the number of people on Earth in the years 1970, 1980, and 1990 was 3710 million, 4450 million, and 5280 million, respectively. Assuming the world population grows logistically, determine (a) the maximum number of people Earth can sustain, and (b) the year in which the population is expected to grow the fastest.
10. A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x = number of units of the product received from Kansas City y = number of units of the product received from Minneapolis
there are 6000 students at mountain high school and 3/4 of these students are seniors,if 2/3 of the seniors are in favor of the school forming a debate team and 1/5 of the remaining students(not seniors) are also in favor of forming a debate team,how many students do not favor this idea?
Suppose that the captain of a ship that is in distress must send a total of twelve different signals in succession. The twelve signals com- prise of 4 blue light signals (B1, B2, B3 and B4), 4 purple light signals (P1, P2, P3 and P4) and 4 red light signals (R1, R2, R3 and R4). He must send the signals one after another at 1 minute intervals. In how many different ways may the captain send the signals if signals of each of the same colour are to be sent consecutively? [Answer]
3. The Phony TV company makes two different types of television sets, OLED and LED, which are assembled by two different assembly lines. When Line One operates it assembles 30 units of the OLED model and 50 units of the LED model per hour. Line Two assembles 40 units of the OLED model and 40 units of the LED model per hour. Let r be the number of hours that Line One operates and y the number of hours Line Two operates. Phony needs to produce at least 3000 units of the OLED model and 4000 units of the LED model to fill an order. (a) Write down the inequalities that describe the assembly constraints. (b) Graph the feasible region determined by these constraints.
In a certain company, the salary of men can take the values of 1,000,000, 1,500,000, 2,000,000 and 2,500,000. Women can enjoy the following salaries: 500,000, 1,000,000, 1,500,000 and 2,000,000. Assuming that the percentage of men earning each of the values is the same, and the same relative to women, and that men's wages are independent of women's wages, what is the probability that a couple, chosen at random, together, earn between 2,000,000 and 3,500,000 (included)?
1. A private telephone company serving a small community makes a profit of 12.00 per subscriber, if it has 725 subscribers. It decides to reduce the rate by a fixed sum for each subscriber over 725, thereby reducing the profit by 1 paise, per subscriber. Thus, there will be profit of 11.99 on each of the 726 subscribers. 11.98 on each 727 subscribers, etc. What is the number of subscribers which will give the company the maximum profit? 2. The lateral edge of a regular rectangular pyramid is a cm long. The lateral edge makes an angle a with the plane öf the base. Find the value of a for which the volume of the pyramid is greatest. 3. A figure is bounded by the curves y=x+ 1, y=0, x=0 and x =. 1. At what point (a, b), a tangent should be drawn to the curve y=: x² +1 for it to cut off a trapezium of the greatest area from the figure. 4. Prove that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3rd the diameter of the sphere. 5. Find…
A supplier for the automobile industry manufactures car and truck frames at two different plants. How many hours should each plant be scheduled to operate to exactly fill each of the orders in the right table? The production rates (in Frames per hour) for each plant are given in the left table. Plant A B Car Frames 2 3 Complete the table below. Number of hours for plant A Number of hours for plant B Truck Frames 4 7 1 Car frames Truck frames ... Orders 2 1 634 1454 3 Orders 2 751 1635 3 848 1846
Suppose a company charges an annual premium of $110 for an insurance policy for minor injuries. Actuarial studies show that in case of an injury claim, the company will pay out an average of $900 for outpatient care and an average of $3000 for an overnight stay in the hospital. They also determine that, on average, each year there are five claims made that result in outpatient care for every 1000 policies and three claims made that result in an overnight stay out of every 1000 policies. What is the expected annual profit of an insurance policy for the company?
Suppose that Jeremy is a highschool science teacher and that he is dividing 16 students in his advanced chemistry class into four groups of four for a lab activity. Each of the four lab groups has been assigned its own task to complete for the activity, but the students are not assigned specific roles within the group. How many different ways can Jeremy assign his students to the four lab groups?
B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ and M2. Each unit of type A requires 1 hour of processing by M₁ and 2 hours in M and each unit type of type B requires 3 hours on M₁ and 1 hour on M₂. The profit on product A is P20 per unit and on product B is P30 per unit. If M₁ is available for 200 hours each month and M₂ for 300 hours, how many units of each type can be manufactured in one month in order to maximize the profits? Requirement: 1) Formulate the linear programming model 2) Solve the linear programming using the graphical method

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