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- A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…The figure shows a bakery's marginal and average cost curves, and its isoprofit curves. The bakery is a price-taker in a large bread market. Suppose the current market price is P₁. Based on this information, which of the following statements is correct? Price, Cost €6 (5 20 40 60 80 Quantity MC hoprofits AC 100 120 140 160 180 number of loaves Select one or more: a. The bakery would be better off raising its price up to its AC level. O b. The bakery would be minimising its loss at A. Oc. If the bakery is not yet in the market then it would not enter the market. d. If the bakery is already in the market, then it would always immediately exit the market because it is making a loss.Suposse a munufacture of widgets has a fixcost of $2500, a variable cost of $30 per widget ans sell 100 widgets for 4,500. Find the cost function C(n) Find the revenue function R(n) Find the profit function P(n)
- A donut shp has a fixed cost of $92000 per day and a varibale cost of $2 for each donut produced. If the donuts are sold to distributors for $5 each. What is the price-demand function? What is the revenue function?Price and cost (dollars per student) $150 120 88 76 72 ATC 40 - MC MR 24,000 30,000 36,000 Quantity of students enroiled 15,000 Your college decides to offer a psychology course as a MOOC that can be taken by students anywhere in the world, whether they are actually enrolled in your college or not. The demand and cost situation for the MOOC is shown in the figure. The faculty member who designed the course argues: "I think the course should be priced so that the maximum number of students enroll." Which price should this faculty member favor? O A. $0 В. $40 C. $88 D. $150(a) How much is total fixed cost? (b) At what output is the price elasticity of demand equal to -1? (c) At what outputs does the firm break even?
- |1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)Lukanga Water has been providing water services in the Central Province for more than 20 years. Business analysts estimated the demand for water is P 40- 5Q, where Q is the number of clients served (in thousands) and P is the price charged (in millions of Kwacha). Lukanga Water total costs are determined as TC = 10 - 0.75Q. (a) How much is the profit maximizing level of output? (b) How much is Price at profit maximizing level of output? (c) Calculate the Profit level.A manufacturer of electric switches in a competitive industry has a fixedmonthly cost of $50,000, total monthly variable cost $100,000, and marginalcost of $5. What is the profit if the monthly production is 100,000 units?Assuming that prices of switches fluctuate from month to month, what is the lowest price the manufacturer can accept in order to stay in business in the long run and in the short run. Will those prices be the same? Show detail work
- Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 10 + 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) %3D P'(x) (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue 2$ profit 2$ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.Question Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…The demand and total profit function, P(x) for rooms in a hotel are given as follows. 3x = 600 - P P(x) = 450x – 3.5x2 - 4000 Where p is the price in ringgit per room and x is the quantity of room rented. Determine the marginal cost when 2 rooms are rented
