Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one). Suppose that a customer ata restaurant spends, on average, R per visit and comes F times each year (for example, if a customer purchases once every two years, then1F-=-0.5. The restaurant realizes a gross profit margin of M (expressed as a fraction) on the average bil for food and drinks. In addition, thefraction of customers defecting (not returning) each year is D. Complete parts a and b.Ta. Develop a mathematical model to compute V, the gross profit during a customer's Metime in doing business with the restaurant (this is oftencalled the economic value of a customer).(Simplify your answer.)b. If the average purchase per visit is $50, the gross profit margin is 0.4 (that is, 40%), customers visit an average of six times each year and30% of customers defect each year, what is the economic value of the customer?The economic value of the customer is $(Round to the nearest dollar as needed.)

(a) We have to develop a mathematical model to compute the gross profit during a customer's lifetime…

Answered: Few companies take the time to estimate…

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 firm produces headphones in two qualities, Basic (B) and Premium (P). For the coming year, the estimated quantity produced of B is 60% higher than that of P. The firm makes a markup of 170% on both products. The ratio between the profits per unit between P and B is 2. The cost price for P is $260. If the profit target is $115 362 over the next year, how much of each of the two qualities must be produced and what are the two selling prices? (Round the quantities to the nearest unit and the prices to 2 digits after the decimal point if needed) Quantity of B = Answer units Quantity of P = Answer units Selling price of B = Answer $ Selling price of P = Answer $
A. Find the average cost function for ? televisions produced. B. Find the instantaneous rate of change of the average cost function.
The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C = (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C( )Calculate the total cost if there are 225…
In a given year, the U.S. federal income tax owed by a married couple filing jointly can be found from the following table. Married Filing Jointly Taxable Income $0-$18,550 T(x) = $18,551-$75,300 $75,301-$151,900 amount over $75,300 $413,351-$466,950 Tax Rate 10% $1,855 plus 15% of the amount over $18,550 $10,367.50 plus 25% of the $151,901-$231,450 amount over $151,900 $466,951 or more if $29,517.50 plus 28% of the $231,451-$413,350 amount over $231,450 $51,791.50 plus 33% of the $130,578.50 plus 39.6% of the amount over $466,950 (a) For incomes up to $151,900, write the piecewise defined function T with input x that models the federal tax dollars due as a function of x, the taxable income dollars earned. $111,818.50 plus 35% of the amount over $413,350 0 < x≤ 18,550 if 18,550 < x≤ 75,300 if 75,300 < x≤ 151,900 (b) Use the function to find T(40,000). $ (c) Find the tax due on a taxable inco of $90,000. $ (d) A friend tells Jack Waddell not to earn any money over $75,300 because it…
It costs a coat manufacturer $8750 to make 125 coats and it costs $6500 to make 80 coats. Each coat is sold for $300. a. How much is the marginal cost? Round to two decimal places if rounding is necessary. b. What is the slope of the Profit function, P(x)? Round to two decimal places if rounding is necessary. c. How many coats must be sold in order to break even? Round to the nearest whole number if rounding is necessary.
Recently there has been a rise in fatal accidents caused by “distracted driving.” The United States National Highway Traffic Safety Administration (NHSTA) defines a distraction as anything that diverts attention from driving. The following model estimates the trend in distracted driving accidents over time based on data from the NHSTA:D = 0.015t - 29.97 In this model, D is the decimal to be turned into a percentage of all fatal accidents caused by distracted driving, and t is any calendar year between 2000 and 2020. Use the model to estimate the rate for 2005 and 2020. Note: this means to plug n 2005 for t and simplify and then turn your answer into a percent. Then plug in 2020 for t and simplify and then turn your answer into a percent.
A graphing calculator is recommended.A dealer predicts that new cars will sell at the rate of 5xe−0.2x sales per week in week x. Find the total sales in the first half year (week 0 to week 26). (Round your answer to the nearest whole number.)
Suppose the total income in dollars from a machine is given by the following. I= 10e0.5t, 0sts 6, tin hours Find the average income (in dollars) over this 6-hour period. (Round your answer to the nearest cent.) $
2. You bought a new computer for $2,500. Four years later, your computer is valued at $1,250. a. Assume that the cost function will be linear and write a linear function to describe the cost of the computer ?t years after you bought it. b. Assume that the cost function will be exponential (think of exponential decay) and write an exponential function to describe the cost of the computer ?t years after you bought it. c. For each function you just wrote, find the rate at which the cost is depreciating 3 years after you bought it. d. Which function do you think would be more accurate? Write a complete sentence or two describing why you think so.
A graphing calculator is recommended. Straight-line depreciation is a method for estimating the value of an asset (such as a piece of machinery) as it loses value ("depreciates") through use. Given the original price of an asset, its useful lifetime, and its scrap value (its value at the end of its useful lifetime), the value of the asset after t years is given by the formula for 0 ≤ t ≤ (Useful lifetime). (a) A farmer buys a harvester for $40,000 and estimates its useful life to be 20 years, after which its scrap value will be $4000. Use the formula above to find a formula for the value V of the harvester after t years, for 0 ≤ t ≤ 20. (Do not use commas in your answer.) V = Value = Price - (b) Use your formula to find the value of the harvester after 5 years. V(5) = No Solution (c) Graph the function found in part (a) on a graphing calculator on the window [0, 20] by [0, 40,000]. (Hint: Use x instead of t.) Help 40000 30000 Price (Scrap value) (Useful Lifetime) 20000 10000 10 Fill…

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