The quantity of a product demanded by consumers is a function of its price. The quantity of one product demanded may also dependon the price of other products. For example, if the only chocolate shop in town (a monopoly) sells milk and dark chocolates, the price itsets for each affects the demand of the other. The quantities demanded, 9₁ and 92, of two products depend on their prices, p₁ and p2,as follows:If one manufacturer sells both products, how should the prices be set to generate the maximum possible revenue? What is thatmaximum possible revenue?Enter the exact answers.P1 =P2 =91 =205 - 4p₁ - 2p₂92 == 250 - 3p₁ - 4p₂.The maximum revenue is

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Answered: The quantity of a product demanded by…

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 collector of antique clocks sold at auction believes that the price received for the clocks may be modeled as a linear function of the age of the clocks and the number of bidders at the auction. After a preliminary study and collection of 32 observations, the collector came up with the following second-order model: y = BO+B₁x₁+B₂x₂ + ß3 x1x2 +B4x² +ɛ, where y: price of a clock; x₁: age of a clock; x2: the number of bidders. Considering the output below and by setting a = 0.05, answer the following questions. The regression equation is Price = 262 +2.26 Age + 14.2 Bidder + 1.13 AgeBid 4.20 Bid^2 Predictor Constant -261.7 2.260 14.21 Age Bidder AgeBid Bid^2 S = 84.512 Coef SE Coef 1.1301 -4.196 Analysis of Variance Source 404.4 2.052 R-Sq= 96.0% Variable Age Bidder AgeBid Bid^2 60.83 0.23 5.17 0.000 0.219 1.344 -3.12 0.004 R-Sq (adj) DF Regression 4 4606950 Residual Error 27 192840 Total 31 4799790 SS T P -0.65 0.523 1.10 0.280 0.817 a. Is the model useful as a whole? Apply an…
Suppose that two variables, say x and y, have a very strong negative linear relationship. By virtue of the fact that the relationship is a STRONG, NEGATIVE, LINEAR relationship, which of the following statements is (are) true? Select ALL that apply. A. If the value of x increases, then we expect the value of y to decrease. B. If the value of x decreases, then we expect the value of y to decrease as well. C. If the value of x decreases, then we expect the value of y to increase. D. If the value of x increases, then we expect the value of y to increase as well.
Three competing brands of cerial are being sold in the school cafeteria. Brand z's weekly sales are affected by the sales of the other two proucts. For each $1 increase in brand æ's sales, there is a decrease $0.80 in sales of brand z. Similarly, each $1 increase in brand y's sales, there is a increase $0.10 in sales of brand z. If the current sales for brand z, y, and z are $45.00, $69.00, and $76.00 respectively, write an equation for z's sales in terms of a and y.
As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table. Price per Pound, p $3.00 $4.00 $5.00 Monthly Sales, q (pounds) 404 286 224 Ae-DP, where A and b are constants you must determine. (a) Use the sales figures for the prices $4 and $5 per pound to construct a demand function of the form q (Round A and b to two significant digits.) q = (b) Use your demand function to find the price elasticity of demand at each of the prices listed. (Round your answers to two decimal places.) p = $3 E = p = $4 E = p = $5 E = (c) At what price should you sell the cheese to maximize monthly revenue? (Round your answer to the nearest cent.) $ (d) If your total inventory of cheese amounts to only 200 pounds and it will spoil one month from now, how should you price it to receive the…

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