4. JACEM makes and sells two competing products, burgers and pizza, that cost $C, and $C, per unit, respectively, to produce. Let R(x, y) be the revenue from marketing x units of burgers and y units of pizzas. Show that if the company's profit is maximized when x = a, y = b, then ƏR (a, b) = C and ƏR (a, b) = Cp ду

4. JACEM makes and sells two competing products, burgers and pizza, that cost $C, and $C, per unit, respectively, to produce. Let R(x, y) be the revenue from marketing x units of burgers and y units of pizzas. Show that if the company's profit is maximized when x = a, y = b, then ƏR (a, b) = C and ƏR (a, b) = Cp ду

Name: 4. JACEM makes and sells two competing products, burgers and pizza,th
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: 4. JACEM makes and sells two competing products, burgers and pizza,thatcost $C, and $C» per unit, respectively, to produce. Let R(x,y) be therevenue from marketing x units of burgers and y units of pizzas. Show thatif the company's profit is maximiz

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A restaurant requires different numbers of full-time employees on different days of the week.Union rules state that each full-time employee must five consecutive days and then two daysoff. The management office wants to meet its daily requirements (Monday: 11, Tuesday: 16,Wednesday: 14, Thursday: 15, Friday: 18, Saturday: 19 and Sunday: 23) using only full-timeemployees. Formulate an LP that the restaurant can use to minimize the number of full timeemployees who must be hired
A private investment club has $200,000 earmarked for investment in stocks. To arrive at anacceptable overall level of risk, the stocks that management is considering have been classifiedinto three categories: high risk, medium risk, and low risk. Management estimates that high-riskstocks will have a rate of return of 15%/year; medium-risk stocks, 10%/year; and low-risk stocks,6%/year. The members have decided that the investment in low-risk stocks should be equal tothe sum of the investments in the stocks of the other two categories. Determine how much theclub should invest in each type of stock if the investment goal is to have a return of$20,000/year on the total investment. (Assume that all the money available for investment isinvested.)Note: Develop the linear system of equations from the above theory and solve the system byGauss Jordon Method.
The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…
A publishing company sells 400,000 copies of a certain book each year. Ordering the entire amount printed at the beginning of the year ties up valuable storage space and capital. However, printing the copies in several partial runs throughout the year results in added costs for setting up each printing run, which costs $1000. The carrying costs, figured on the average number of books in storage, are $.50 per book. Find the most economical lot size, that is, the production run size that minimizes the total setting up andcarrying costs.
A group of medical professionals is considering theconstruction of a private clinic. If the medical de-mand is high (i.e., there is a favorable market for theclinic), the physicians could realize a net profit of$100,000. If the market is not favorable, they couldlose $40,000. Of course, they don’t have to proceedat all, in which case there is no cost. In the absenceof any market data, the best the physicians can guessis that there is a 50–50 chance the clinic will be suc-cessful. Construct a decision tree to help analyze thisproblem. What should the medical professionals do?
Suppose that a company needs 5 ×10,000 items during a year and that preparation costs are $5 for each production run. Suppose further that it costs the company $3 to produce each item and $2 to store an item for up to a year. If each production run consists of x items, find x so that the total costs of production and storage are minimized. How did you verify that the amount found in the this problem was a minimum? It is not sufficient to just identify then process, you must explain how it applied to this problem in particular.
A firm has 2 plants with different functions: - Plant 1: MC = 30 + Q - Plant 2: MC = 20 + 2Q How to allocation output between the 2 plants to minimize total cost of producing 50 units of output? What is the minimum total cost?
Assume that each full team consists of 1 doctor and 5 nurses, and that each half team consists of 1 doctor and 3 nurses. Assume also that there are 220 doctors and 920 nurses available to serve on teams. Assume also that the each full team can inoculate 240 people per hour and that each half team can inoculate 140 people per hour. How many full teams and half teams should be formed in order to maximize the number of inoculations per hour?
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $5/unit of Product A and a profit of $7/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?
A pharmaceutical firm wishes to allocate Php50,000 towards advertising in newspapers and magazines. The intention of the firm is to maximize the exposure of its advertisements. Each page of the leading newspapers costs Php500 and each page of the magazine costs Php1,000. It is guaranteed that each page of the magazine will reach an audience of 250,000, while 50,000 persons will read each page of the newspaper advertisement. Furthermore, it is specified that at least one page of the magazine and newspaper will be allocated for the firm's advertisement. Find the number of pages of magazine advertisement that will maximize exposure and still remain within the Php50,000 budget. Solve using graphical method. Newspaper Magazine Limitations 1 1 1. 500 1000 50,000 50,000 250,000
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $6/unit of Product A and a profit of $4/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x, y) = What is the optimal profit? (Round your answer to the nearest whole number.)
A manufacturer produces two models of racing bike, X and Y, each of which must be processed through two machine shops. Machine shop 1 is available for 100 hours per month and machine shop 2 for 160 hours per month. The manufacture of each bike of type X takes 6 hours in shop 1 and 3 hours in shop 2. The corresponding times for Y are 4 and 10 hours respectively. If the profit is $160 and $200 per bike of type X and Y respectively, how should the manufacturer arrange production to maximize total profit?