A street vender constructs the table below on the basis of sales data. (Note: Consumer expenditure and revenue are terms for the same thing from different perspectives. Consumer expenditure is the amount of money that consumers spend on a product, and revenue is the amount of money that businesses take in by selling the product.) Sales of Roses, Given the Price per Dozen Sales (dozen roses) Price (dollars) 20 25 30 32 169 159 134 94 (a) Find a quadratic function for the model of the data that gives the quantity sold at x dollars, data from 20 sxs 32. (Round all numerical values to three decimal places) S(x)= (b) Find a function for the model for consumer expenditure (revenue for the vendor), where x is the price in dollars, data from 20 sxs 32. (Round all numerical values to three decimal places.) R(x)=

A street vender constructs the table below on the basis of sales data. (Note: Consumer expenditure and revenue are terms for the same thing from different perspectives. Consumer expenditure is the amount of money that consumers spend on a product, and revenue is the amount of money that businesses take in by selling the product.) Sales of Roses, Given the Price per Dozen Sales (dozen roses) Price (dollars) 20 25 30 32 169 159 134 94 (a) Find a quadratic function for the model of the data that gives the quantity sold at x dollars, data from 20 sxs 32. (Round all numerical values to three decimal places) S(x)= (b) Find a function for the model for consumer expenditure (revenue for the vendor), where x is the price in dollars, data from 20 sxs 32. (Round all numerical values to three decimal places.) R(x)=

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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The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. Year 2012 2013 Selling Price ($) 395 325 Sales (millions) 741 1,133 (a) Use the data to obtain a linear demand function for this type of cell phone. (Let p be the price, and let q be the demand). q(p) = Use your demand equation to predict sales if the price is lowered to $255. million phones (b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by million units.
The table shows the approximate increase in sales that an additional $100 spent on advertising, at various levels, can be expected to generate. Increase in Revenue Due to an Extra $100 Advertising When Advertising Is Already at a Given Level Expenditures, x (hundred dollars) 25 50 75 100 125 150 175 Revenue Increase, R (thousand dollars) 4 59 94 107 104 78 33 (a) Find the function of the quadratic model that gives the approximate increase in revenue in thousand dollars per hundred dollars that occurs when an additional $100 is spent on advertising, where x is the amount in hundred dollars already spent on advertising, with data from 25 ≤ x ≤ 175. (Round all numerical values to three decimal places.) R'(X) = thousand dollars per hundred dollars (b) Use the model in part (a) to write the function of the model for the total sales revenue R in thousand dollars when x hundred dollars is spent on advertising. Use the fact that revenue is approximately $876,000 when $5000 is spent on…
Please complete part (a) and part (c). Circle your answer for a thumbs up :)
The demand for a 12-ounce bottle of sparkling water is given in the table. Demand Schedule for Sparkling Water in 12-ounce Bottles Price (dollars per bottle) 2.29 2.69 3.09 3.49 3.89 4.29 Demand (million bottles) 25 9 3 2 1 0.5 (a) Write the function for the exponential model that gives demand in million bottles, as a function of price per bottle p, with data from 2.29 s ps 4.29. (Round all numerical values to two decimal places. Be sure you use the correct input variable p.) D(p) = Does the model indicate a price above which consumers will purchase no bottles of water? The model is exponential and ---Select--- the horizontal axis. Therefore there is --Select--- above which consumers will not purchase water. (b) What quantity of water will consumers purchase when the market price is $4.09? (Round your answer to two decimal places.) million bottles (c) Calculate the amount that consumers willing and able to spend to purchase the quantity found in part (b). (Round your answer to one…
The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x) = 56x – 0.020x? 0sxs 2800 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (Round to one decimal place as needed.) (B) R'(X) = (C) R(1000) = R'(1000) = Interpret these results. Choose the correct answer below. O A. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. O B. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. O c. This means that at a…
The demand for a 12-ounce bottle of sparkling water is given in the table. Demand Schedule for Sparkling Water in 12-ounce Bottles Price (dollars per bottle) 2.29 2.69 3.09 3.49 3.89 4.29 Demand (million bottles) 25 9 3 2 1 0.5 (a) Write the function for the exponential model that gives demand in million bottles, as a function of price per bottle p, with data from 2.29 ≤ p ≤ 4.29. (Round all numerical values to two decimal places. Be sure you use the correct input variable p.) D(p) = Does the model indicate a price above which consumers will purchase no bottles of water? The model is exponential and ---Select--- ✓the horizontal axis. Therefore there is ---Select--- above which consumers will not purchase water. (b) What quantity of water will consumers purchase when the market price is $3.87? (Round your answer to two decimal places.) million bottles (c) Calculate the amount that consumers willing and able to spend to purchase the quantity found in part (b). (Round your answer to one…
Quadratic Functions #2 (in image)
A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 34 feet. If the distance across the top of the mirror is 70 inches how deep is the mirror in the center? A) 1225/19584 in. B) 289/35 in. C) 1225/1632 in. D) 1225/136 in. Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations. x = t^3 + 1, y = t^3 - 15; -2 lessthanorequalto t lessthanorequalto 2 A) y = x - 16; -7 lessthanorequalto x lessthanorequalto 9 B. y = -x^2; -4 lessthanorequalto x lessthanorequalto 4 C) y = -x - 16; -7 lessthanorequalto x lessthanorequalto 9 D) y = x^3; -3 lessthanorequalto x lessthanorequalto 1 Solve the problem. Round to the nearest if needed. To save for retirement, you decide to deposit $2000 into an IRA at the end of each year for the next 40 years. If the interest rate is 9% per year compounded annually, find the value of the IRA after 40 years. A) $60, 819 B) $24, 330, 719 C) $675, 765 D) $618, 133…
Advertising A small manufacturing firm collected the following data on advertising expenditures A (in thousands of dollars) and total revenue R (in thousands of dollars). (a) Draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables (b) The quadratic function of best fit to these data is R(A) = - 7.76A2 + 411.88A + 942.72 Use this function to determine the optimal level of advertising. (c) Use the function to predict the total revenue when the optimal level of advertising is spent. (d) Use a graphing utility to verify that the function given in part (b) is the quadratic function of best fit. (e) Use a graphing utility to draw a scatter diagram of the data, and then graph the quadratic function of best fit on the scatter diagram.
Please solve this
As the selling price of a product increases, demand decreases. Fewer people will buy a product if it is more expensive. This is a very important concept. The demand equation for new iSmarts is given by 0.025x , where p is the unit p = 100 price (in dollars) of the iSmart and x is the number of units produced. We can determine the total revenue (money earned for selling x iSmarts) by multiplying the number of items we sell, x and the price p. The total revenue obtained by producing and selling x iSmarts is given by = xp 100x – 0.025x². It makes sense that this function is quadratic. The company can price the iSmarts so high that no one will buy them and the revenue will be zero. The can also set the price to $0, but the revenue will still be $0, no matter how many iSmarts they "sell". In between, the graph is a parabola opening downward. Determine prices p that would keep revenue above 6530 dollars. Give your answers to 2 decimal places. The revenue will be above 6530 if price is…
The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=64x-0.020x² 0≤x≤3200 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. ... (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 23 (Round to one decimal place as needed.) (B) R'(x) =