Revenue Function The management of Lorimar Watch Company has determined that the daily marginal revenue function associated with producing and selling their travel clocks is given by R'(x) = -0.002x + 8 where x denotes the number of units produced and sold and R(x) is measured in dollars/unit. (a) Determine the revenue function R(x) associated with producing and selling these clocks. R(x) = (b) What is the demand equation that relates the wholesale unit price p with the

Revenue Function The management of Lorimar Watch Company has determined that the daily marginal revenue function associated with producing and selling their travel clocks is given by R'(x) = -0.002x + 8 where x denotes the number of units produced and sold and R(x) is measured in dollars/unit. (a) Determine the revenue function R(x) associated with producing and selling these clocks. R(x) = (b) What is the demand equation that relates the wholesale unit price p with the

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 8PS

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Maximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.
Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
The demand function for the Viking Boat’s 34-ft Sundancer yacht isp = 200 − 0.01x ln x,where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.(a) Find the revenue function and the marginal revenue function for this model of yacht.(b) Use the result of part (a) to estimate the revenue realized from the sale of the 500-th34-ft Sundance yacht. (Note: This is an estimate, so be careful to use the correct functionfrom part (a) and to evaluate it at the correct value of x.)(c) Now compute the exact revenue realized from the sale of the 500-th 34-ft Sundance yacht. (d) Comment on the approximation provided in part (b).
Marginal Cost Functions The management of National Electric has determined that the daily marginal cost function associated with producing their automatic drip coffeemakers is given by C'(x) = 0.00003x2 − 0.03x + 24 where C'(x) is measured in dollars per unit and x denotes the number of units produced. Management has also determined that the daily fixed cost incurred in producing these coffeemakers is $900. What is the total cost incurred by National in producing the first 500 coffeemakers/day?
Temperature between fluids in a heat exchanger used to heat a medium Based on the difference (X) (X> 2) the annual fuel cost (Y1) and the annual investment cost (Y2) are given as. Determine the temperature difference that will minimize the annual total cost (Y) Y1 = 6X2 - 10X + 5000 Y2 = 25000 - X2 - 140X
The total cost and the total revenue (in dollars) for the production and sale of x ski jackets are given by C(x)=28x+37,960 and R(x)=200x−0.1x2 for 0≤x≤2000. (A) Find the value of x where the graph of R(x) has a horizontal tangent line. (B) Find the profit function P(x). (C) Find the value of x where the graph of P(x) has a horizontal tangent line. (D) Graph C(x), R(x), and P(x) on the same coordinate system for 0≤x≤2000. Find the break-even points. Find the x-intercepts of the graph of P(x).
Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is p = 300 − 0.01x ln(x) where x denotes the number of yachts and p is the price per yacht in hundreds of dollars. (a) Find the revenue function R(x) and the marginal revenue function R'(x) for this model of yacht. R(x) = R'(x) = (b) Use the result of part (a) to estimate the revenue to be realized from the sale of the 425th 34 ft Sundancer yacht. (Round your answer to the nearest dollar.) $_________
(Please give a clear and elaborate solution) A company determined that the price-demand and cost functions for selling x units of a certain product are given byp(x) = x2 − 10x + 3,600 and C(x) = x3 + 2,450, respectively, where p and C are in pesos. Find the marginal profit when 200 units of the product are sold.
A company can manufacture at most 200 units per month. About x units per month can be sold at the price p(x) = (500 – x) dollars and the cost of producing x units per week is C(x) = 150 + 4x + x2 dollars. Find; a. Revenue from sale of x units per week b. Maximum weekly profit and the number of units produced to obtain the maximum d. Marginal Revenue at Maximum weekly profit level c. Marginal cost functions at Maximum weekly profit level
The monthly revenue associated with renting a total of x apartments is R(x)=1,500−.4x2 . The monthly cost associated with renting a total of x apartments C(x)=25,000+600x. Find the profit function, P(x). b. Find the marginal profit function
Marginal Cost A division of Ditton Industries manufactures a deluxe toaster oven. Management has determined that the daily marginal cost function associated with producing these toaster ovens is given by C'(x) = 0.0006x2 − 0.14x + 23 where C'(x) is measured in dollars per unit and x denotes the number of units produced. Management has also determined that the daily fixed cost incurred in the production is $900. Find the total cost incurred by Ditton in producing the first 300 units of these toaster ovens per day. What is the total cost incurred by Ditton in producing the 201st through 300th units/day?
The daily cost per unit of producing a product by the Ace Company is 15 + 0.2x dollars and the price on the competitive market is $80. Find the revenue function, cost function, profit function, and marginal profit function (in dollars). R(x) = C(x) = P(x) = MP = What is the maximum daily profit the Ace Company can expect on this product? $