3. A company with monopolistic control in the market has fixed weeklycosts of $5,000 and per unit costs of $(210+0.05x), where x representsthe number of units produced. The weekly demand for x units dependsupon the price set by the company. At a price of $300 there will beno demand, but demand increases by one unit for each cent less than$300 the price is set at.(a) Write down the equation for the weekly cost function C(x) andweekly demand function p(x) (price as a function x).(b) What price should the company set to maximise its profit?

A company with monopolistic control in the market has fixed weekly cost of $5000 and per unit costs…

Answered: 3. A company with monopolistic control…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Similar questions

Suppose demand is given by p = 1600 − x. Find the maximum revenue.
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.
Solve these :
Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. consumer price index (CPI) can be modeled by the function y = 0.0682x² + 1.76x + 96.0 where x is the number of years past 2010 and y is the CPI in dollars. With a reference of 100 in 2012, a CPI of 120 in another year means that goods and services costing $100 in 2012 are expected to cost $120 in that other year (a) Use a table to determine a viewing window that shows a complete graph of this function for the years from 2010 to 2050. 2050 corresponds to an x value of which corresponds to a y value of The y maximum should be -Select-than this function value (b) Graph the function. y 300 250 200 150 100 50 0 y 300 250 200 150 100 50 X = Need Help? 51 F Partly sunny 10 10 20 Read It 20 30 30 T X 40 40 y 300 250 200 150 100 50 0 0 10 (c) Use the graph to estimate when the CPI is predicted to reach 250. (Round your answer to the nearest whole year.) years 20 30 Q Search 40 y 300 250 200…
If x represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c) state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of items), and (e) support the results of part (d) graphically. The fixed cost is $600, the cost to produce an item is $25, and the selling price of the item is $50. (a) The cost function is C(x) = (Simplify your answer. Do not factor.) (b) The revenue function is R(x)= (Simplify your answer. Do not factor.) (c) The profit function is P(x) = (Simplify your answer. Do not factor.) ← (d) At least items must be produced before a profit is shown. (Type a whole number.) (e) Choose the correct graph to the right. O A. 2100 O C. Dollars Items produced 2100 Items produced Q O B. 2100 O D. Dollars 2100 Items produced Items produced Q ✔
The manufacturing laundry sinks has fixed costs if $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q =360 – p, where q is the number of laundry sinks demanded and p is the price of a laundry sink. 1. If we assume that the total cost per day is linearly related to the amount of sinks produced in a day, derive the total cost function of the company? 2. Find a function for the average cost of this company

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