Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive, then more people will buy the other. If p, is the price of the Ultra Mini and P2 is the price of the Big Stack, demand for the Ultra Mini is given by 91 (P1, P2) = 50,000 – 100p1 + 10p2 %3D where q, represents the number of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by 92 (P1. P2) = 150,000 + 10p, – 100p2 92 represents the number of Big Stacks that will be sold in a year. Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. where

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive, then more people will buy the other. If p, is the price of the Ultra Mini and P2 is the price of the Big Stack, demand for the Ultra Mini is given by 91 (P1, P2) = 50,000 – 100p1 + 10p2 %3D where q, represents the number of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by 92 (P1. P2) = 150,000 + 10p, – 100p2 92 represents the number of Big Stacks that will be sold in a year. Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. where

Name: Your company manufactures two models of stereo speakers, the Ultra Mi
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Your company manufactures two models of stereo speakers, the Ultra Miniand the Big Stack. Demand for each depends partly on the price of the other. If one isexpensive, then more people will buy the other. If p, is the price of the Ultra Mini andP2 i

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

Related questions

Q: A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a…

A: From the given data:x1=200+100p2-p1 and x2=500-150p2Total…

Q: Pearson's r ranges from -1.00 (the strongest possible negative relationship) to + 1.00 (the…

A: Correlation: The correlation is used to measure the strength of the association between variables.

Q: 6x2 -4x 1. Find the first-order derives: I. y II. y = (2x3 + 7x – 14)5 %3D 4x2-8x+5

A: To find the first-order derivative of the given function using the quotient rule and chain rule…

Q: An engineer creates a model to predict the electric consumption of a household in summer in a day…

A: # consider a linear regression model y=b0+b1*X b0=23 hr & b1=1.55 hr then to find y at x=17…

Q: An engineer creates a model to predict the electric consumption of a household in summer in a day…

A: Depending the type of relation between the variables, the regression models are designed. If there…

Q: I like to take in account how much I’m going to set aside for savings that month as well as…

A: If a person saves $400 per month and spends $1000 on bills per month then let 'x' be the number of…

Q: On the sixth day of having the sea monkeys, when the population was approximately 68, Penny couldn't…

Q: Sales of fine-cut cigarettes (in millions) in a country are given by y = - 14.898x2 + 356.467x +…

Q: You are planning a rectangular patio measuring 12 feet wide and 14 feet long with one edge running…

A: Properties of rectangle are Opposite sides are equal and parallel Diagonals are equal and bisect…

Q: A manufacturer of hot tubs makes two kinds of hot tubs - Bill and Jane. Bill requires 8 hours of…

A: Given that bill hot tub requires 8 hours of labor and Jane hot tub requires 12 hours of labor.Also…

Q: ABC Company makes and sells stuffed animals. One product, Michael Bears, sells for $28 per bear. It…

A: We are given with the variable cost and the cost per unit and we have to find the TC risk cost and…

Q: A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a…

A: Given that the cost of production of 1 unit of solid soap is 10 cents = 0.1 dollars and the cost of…

Q: 2x-3y=1 -6x+9y=-3

Q: The cost of a class field trip is $15 per person, plus $50 for a bus ride. Which function can be…

A: Given Per person charge =$15 So charge for x students = 15x Additional charge = $50

Q: A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a…

A: Given that the cost of production per soap is 10 cents and that per liquid soap is 20 cents. Let x1…

Q: The Hydro water department has a monthly service charge of $15 10 and a volume charge of $2 25 for…

A: Let y1 be the monthly cost of the family income in the last month. Let y2 be the monthly cost of the…

Q: (i) Y = ax + b

Q: The revenue function of a company that sells its product at a fixed price of OMR 220 per unit and…

A: Solution

Q: Civil engineers often use the straight-line equation, y = bo+b 1x, to model the relationship between…

A: According to the question, variables x and y denote the shear strength and precompression stress…

Topic Video

Question

Your company manufactures two models of stereo speakers, the Ultra Mini
and the Big Stack. Demand for each depends partly on the price of the other. If one is
expensive, then more people will buy the other. If p, is the price of the Ultra Mini and
P2 is the price of the Big Stack, demand for the Ultra Mini is given by
91 (P1, P2) = 50,000 – 100p1 + 10p2
%3D
where q, represents the number of Ultra Minis that will be sold in a year. The demand
for the Big Stack is given by
92 (P1. P2) = 150,000 + 10p, – 100p2
92 represents the number of Big Stacks that will be sold in a year. Find the prices
for the Ultra Mini and the Big Stack that will maximize your total revenue.
where

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Solution:

VIEW

Obtain the critical point as follows:

VIEW

Solve the equations:

VIEW

Conclusion:

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

An engineer creates a model to predict the electric consumption of a household in summer in a day with a predictor variable of the number of hours the air-conditioner is running. The electric consumption is only at 26 kWh per day if aircon is not used. If the aircon was used by 1 hr, the electric consumption would increase by an additional 1.44 kWh. Find the average electric consumption if the aircon is used 15 hrs.
The percent of high school students who smoked cigarettes on 1 or more of the 30 days preceding the survey is given by y = -0.064x² +0.277x +33.715, where x is the number of years after 1990. During what years from 1990 on is the percent greater than 30%? From to the percent is greater than 30%. (Round up to the nearest year as needed.)
The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000) and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. Square Footage (100 ft’) x2 Income Price ($1000) x1 ($1000) y 80 21 180 150 28 250 75 18 160 a. Use the data to write a system of linear equations to solve for a, b, and c. b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y = ax1 + bx2 + c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.
Find the equation of line (L) that passes through the intersection point of the two functions y = v2 - x2 and y - 2x +3 = 0 and perpendicular to the line %3D 2x – 4y = 6 -
Jane collects data from 40 elementary school students and finds that the relationship between age (x) and score on a certain test (y) is given by y=3.2x+45. What can she extrapolate about the score a 16-year old will get on the test?
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.
Jim's Camera shop sells two high-end cameras, the Sky Eagle and Horizon. The demands for these two cameras are as follows: D = demand for the Sky Eagle, Ps is the selling price of the Sky Eagle, D is the demand for the Horizon, and PH is the selling price of the Horizon. Ds = 223 -0.60PS +/0.35PH DH = 273 +0.10PS - 0.64PH The store wishes to determine the selling price that maximizes revenue for these two products. Develop the revenue function for these two models. (Enter your answer in terms of P and P.) revenue = Find the prices that maximize revenue. (Round your answers to two decimal places.) (PS, PH) =