Please solve this A manufacturer has been selling 1100 QLED televisions a week at $540 each. A market survey indicates that for each $32 discount offered to a buyer, thetotal number sold will increase by 320 TVs per week.We will define the variable a to represent the number of $32 discounts that are offered. We will allow a to be any real number, including decimal values.(a) Find the function p(a) which gives the price of a television in dollars, where a is the number of discounts.p(a) =(b) Find the function q(a) which gives the quantity of televisions sold (the weekly demand), where a is the number of discounts.q(a) =(c) Find the total revenue function R(a) which gives the weekly revenue in dollars, where a is the number of discounts.R(a) =(d) Find the value of a that will maximize the weekly revenue function R(a). Do not round your answer.The value of a to maximize weekly revenue is a =(e) Use your answers above to complete the following sentences. Round each answer to the nearest whole dollar.In order to maximize weekly revenue from the sale of QLED televisions, the manufacturer should discount the current price by a total of $The new price will be $which will generate a weekly revenue of $(1) Still using the a variable defined above, now suppose the weekly cost in dollars is given by the function C(a) = 297000 + 57600a. Determine thevalue of a that will maximize the weekly profit. Do not round your answer.The value of a to maximize weekly profit is a(a) Use your answers above to complete the following sentences. Round each answer to the nearest whole dollar.In order to maximize weekly profit from the sale of QLED televisions, the manufacturer should discount the current price by a total of $The new price will be $which will generate a weekly profit of $

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A manufacturer has been selling 1100 QLED televisions a week at $540 each. A market survey indicates that for each $32 discount offered to a buyer, the total number sold will increase by 320 TVs per week. We will define the variable a to represent the number of $32 discounts that are offered. We will allow a to be any real number, including decimal values. (a) Find the function p(a) which gives the price of a television in dollars, where a is the number of discounts. p(a)= (b) Find the function q(a) which gives the quantity of televisions sold (the weekly demand), where a is the number of discounts. q(a)= (c) Find the total revenue function R(a) which gives the weekly revenue in dollars, where a is the number of discounts. R(a) =

A manufacturer has been selling 1100 QLED televisions a week at $540 each. A market survey indicates that for each $32 discount offered to a buyer, the total number sold will increase by 320 TVs per week. We will define the variable a to represent the number of $32 discounts that are offered. We will allow a to be any real number, including decimal values. (a) Find the function p(a) which gives the price of a television in dollars, where a is the number of discounts. p(a)= (b) Find the function q(a) which gives the quantity of televisions sold (the weekly demand), where a is the number of discounts. q(a)= (c) Find the total revenue function R(a) which gives the weekly revenue in dollars, where a is the number of discounts. R(a) =

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 8E

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A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result, only 40 units were sold in a week. The manufacturers fixed costs of production are $1,710 a week and variable costs are $9 per unit. You are required to: d. Assuming a sudden change in trading conditions resulting in a 20% reduction in demand at all price levels, to find the equation of the new demand function and to recommend how the manufacturer should respond.
Q2 The manufacturer of a low-sugar bottled juice estimated the following demand equation for its product using data from 25 retail stores around Dover city for the month of November: Q=-2000-15 Pje+ 8.4Px + 0.51 + 0.4A (220) (5.0) (5.6) (0.2) (0.16) R²=0.57 n=25 F = 6.83 Assume the following values for the independent variables: Standard error 1 Q denotes quantity sold per month Pje (denotes price of the bottled juice) = 240 (in cents) P. (denotes price of leading competitor's product) - 300 (in cents) I (denotes per capita income of the standard residential district in which the retail store is located) = 4000 (in dollars) A (denotes monthly advertising expenditure) = 7700 (in dollars) Using this information, answer the following questions: a. Compute elasticities for each variable.. b. Do you think that this firm should cut its price to increase its market share?
Q2 The manufacturer of a low-sugar bottled juice estimated the following demand equation for its product using data from 25 retail stores around Dover city for the month of November: Q=-2000-15 Pje+ 8.4Px + 0.51 + 0.4A (220) (5.0) (5.6) (0.2) (0.16) R²=0.57 n=25 F = 6.83 Assume the following values for the independent variables: Standard error 1 Q denotes quantity sold per month Pje (denotes price of the bottled juice) = 240 (in cents) P. (denotes price of leading competitor's product) - 300 (in cents) I (denotes per capita income of the standard residential district in which the retail store is located) = 4000 (in dollars) A (denotes monthly advertising expenditure) = 7700 (in dollars) Using this information, answer the following questions: a. Compute elasticities for each variable.. b. Do you think that this firm should cut its price to increase its market share? Explain..
in excel Price Demand 2000 4500 2800 3600 3500 1850 4000 1200 5000 820 Based on the data above estimate the demand function. When you estimate demand curve, please compare the following options and choose the one with highest R square Exponential Linear Power
ATV is a price-setting firm and estimates the demand for its cement using a demand function in the linear form: Q = f( P, M, PR) where Qc = demand for cement/month (in yards) Pc = the price of cement per yard, M = country’s tax revenues per capita, and PR = the price of asphalt per yard. DEPENDENT VARIABLE Qc R- SQUARE P- VALUE ON F 64 0.8093 0.0001 INDEPENDENTVARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 8.20 4.01 2.04 0.0461 PC -3.54 1.64 -2.16 0.0357 M 0.64287 0.19 3.38 0.0014 PA 0.7854 0.38 2.07 0.0439 10. Write the resulting regression equation.
The profit,P,of a company that manufactures and sells N units of a certain product is modeled by the function P(N)=R(N)-C(N) The revenue function,R(N)=S·N, is the selling price S per unit times the number N of units sold. The company's cost,C(N)= Co +Cop(N), is a sum of two terms. The first is a constant Co describing the initial investment needed to set up production. The other term, Cop(N), varies depending on how many units the company produces, and represents the operating costs. Companies care not only about profit, but also marginal profit, the rate of change of profit with respect to N. Assume that S=$50,Co=$75,000, Cop(N)=$50✓N,and that the company currently sells N= 100 units. Compute the marginal profit at this rate of production.Round your answer to one decimal place.
using the graphical solution procedure, Compute the range of optimality for the objective function coefficients.
A company estimated that the relationship between the unit price and demand per month for a potential new product is approximated by P = $ 100 – $ 0.1D. The company can produce the product by increasing fixed costs $ 17,500 per month, and the estimated variable costs is $ 40 per unit. What is the optimal demand, D*, and based on this demand, should the company produce new product? Why? a) Work out the complete solution by differential calculus, starting with formula for profit or loss per month b) Solve graphically for an approximate answer
Please solve questions 15, 16 and 17. The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = 10000 - 25Pg + 20Ph + 30Pr - 15dv - 35Psc - 10Pmm + 0.05Ag + 0.03A -25C + 0.1Y Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is…
The demand function for Newton’s Donuts has been estimated as follows:Qx = -14 – 54Px + 45Py + 0.62Ax where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company’s goal)? Should Newton’s Donuts spend…
The multivariate demand function below will be needed for questions 12-18. Setting: Grapple, Inc. is a leading seller of laptop personal computers. However, they want to become a leading tablet seller, too. Your marketing department, aided by your economics staff, has estimated a function to help you in the quest for market leader in tablets. The variables are defined after the function. Qg = 10000 - 25Pg + 20Ph + 30Pr - 15dv - 35Psc - 10Pmm + 0.05Ag + 0.03A -25C + 0.1Y Qg = the number of Grapple tablet computers demanded per week. Pg = the price of each new Grapple tablet (in $). Ph = the price of each Hewpaq tablet (in $). Pr = the price of each Ronova tablet. Pdv = the price to equip a tablet with Holographic digital video (in $, this is an upgrade option that enables three-dimensional graphics on a tablet. Two-dimensional graphics is standard equipment). Psc = the price of various screen sizes (in $, a 8 inch is standard, but upgrade options are 10…
From a certain place K, 2000 people set off for work in the distant place S in the morning by car. Each of the drivers must decide whether to come to place S via point G or via point D (see the directed graph below). The travel time on segments G-S and K-D is not dependent on the number of drivers: each driver traverses the G-S segment in 60 minutes, and the K-D segment in 45 minutes, regardless of the number of drivers. However, the travel time on segments K-G and D-S depends on the number of drivers: if x drivers travel on the K-G segment, each driver on this segment consumes 0.005x minutes; if x drivers travel on the D-S segment, each driver on this segment consumes 0.01x minutes (see the directed graph below). Assume that all people start simultaneously and do not know the decisions of other people. Find all pure Nash equilibria of the game.