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he table shows both the number of a certain type of graphing calculator in demand and the number supplied at certain prices. Demand and Supply Schedules for a Graphing Calculator (Producers will supply no calculators when the market price is less than $47.50.) Demand (million calculators) Supply (million calculators) 35 31 15 5 Price (dollars per calculator) 60 90 S(p) = 120 150 180 210 3 10 32 50 80 100 (a) Find the function for the logistic model for demand in million calculators, where p is the price per calculator in dollars, with data from 60 sps 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into D(P) = million calculators million calculators; 120 Find the function for linear model for supply in million calculators, where p is the price per calculator in dollars, with data from 60 s ps 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y2.) for p < 47.5 for p 2 47.5 p dollars per calculator, where 60 sps 210. Tip: Be sure you are using the unrounded demand and supply functions for the calculations that follow. Using the rounded functions may result in incorrect answers. (b) At what price will market equilibrium occur? (Round your answer to two decimal places.) per calculator How many calculators will be supplied and demanded at this price? (Round your answer to two decimal places.) million calculators (c) Calculate the producer surplus at market equilibrium. (Round your answer to three decimal places.) million

he table shows both the number of a certain type of graphing calculator in demand and the number supplied at certain prices. Demand and Supply Schedules for a Graphing Calculator (Producers will supply no calculators when the market price is less than $47.50.) Demand (million calculators) Supply (million calculators) 35 31 15 5 Price (dollars per calculator) 60 90 S(p) = 120 150 180 210 3 10 32 50 80 100 (a) Find the function for the logistic model for demand in million calculators, where p is the price per calculator in dollars, with data from 60 sps 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into D(P) = million calculators million calculators; 120 Find the function for linear model for supply in million calculators, where p is the price per calculator in dollars, with data from 60 s ps 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y2.) for p < 47.5 for p 2 47.5 p dollars per calculator, where 60 sps 210. Tip: Be sure you are using the unrounded demand and supply functions for the calculations that follow. Using the rounded functions may result in incorrect answers. (b) At what price will market equilibrium occur? (Round your answer to two decimal places.) per calculator How many calculators will be supplied and demanded at this price? (Round your answer to two decimal places.) million calculators (c) Calculate the producer surplus at market equilibrium. (Round your answer to three decimal places.) million

Advanced Engineering Mathematics
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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The table shows both the number of a certain type of graphing calculator in demand and the number supplied at certain prices. Demand and Supply Schedules for a Graphing Calculator (Producers will supply no calculators when the market price is less than $47.50.) Demand (million calculators) Supply (million calculators) 35 10 31 32 15 5 Price (dollars per calculator) 60 S(p) = 90 120 150 180 210 4 3 for p ≥ 47.5 p dollars per calculator, where 60 < p ≤ 210. 50 million calculators; 80 (a) Find the function for the logistic model for demand in million calculators, where p is the price per calculator in dollars, with data from 60 ≤p ≤ 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y1.) D(P) = million calculators 100 Find the function for linear model for supply in million calculators, where p is the price per calculator in dollars, with data from 60 ≤p ≤ 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y2.) for p < 47.5 120 Tip: Be sure you are using the unrounded demand and supply functions for the calculations that follow. Using the rounded functions may result in incorrect answers. (b) At what price will market equilibrium occur? (Round your answer to two decimal places.) $ per calculator How many calculators will be supplied and demanded at this price? (Round your answer to two decimal places.) million calculators (c) Calculate the producer surplus at market equilibrium. (Round your answer to three decimal places.) million $ Calculate the consumer surplus at market equilibrium. (Round your answer to three decimal places.) million $ Calculate the total social gain at market equilibrium. (Round your answer to three decimal places.) million $
Transcribed Image Text:The table shows both the number of a certain type of graphing calculator in demand and the number supplied at certain prices. Demand and Supply Schedules for a Graphing Calculator (Producers will supply no calculators when the market price is less than $47.50.) Demand (million calculators) Supply (million calculators) 35 10 31 32 15 5 Price (dollars per calculator) 60 S(p) = 90 120 150 180 210 4 3 for p ≥ 47.5 p dollars per calculator, where 60 < p ≤ 210. 50 million calculators; 80 (a) Find the function for the logistic model for demand in million calculators, where p is the price per calculator in dollars, with data from 60 ≤p ≤ 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y1.) D(P) = million calculators 100 Find the function for linear model for supply in million calculators, where p is the price per calculator in dollars, with data from 60 ≤p ≤ 210. (Round all numerical values to three decimal places. Use the correct input variable, p. Paste the unrounded equation into your Y2.) for p < 47.5 120 Tip: Be sure you are using the unrounded demand and supply functions for the calculations that follow. Using the rounded functions may result in incorrect answers. (b) At what price will market equilibrium occur? (Round your answer to two decimal places.) $ per calculator How many calculators will be supplied and demanded at this price? (Round your answer to two decimal places.) million calculators (c) Calculate the producer surplus at market equilibrium. (Round your answer to three decimal places.) million $ Calculate the consumer surplus at market equilibrium. (Round your answer to three decimal places.) million $ Calculate the total social gain at market equilibrium. (Round your answer to three decimal places.) million $
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