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- A7 You are the manager of a bakery that produces and packages gourmet muffins, and you currently sell muffins in packages of 3. A consultant’s report has estimated the (inverse) demand of a typical consumer to: P = 3 − 0.5Q If your cost of producing bran muffins is C(Q) = Q: (a) What is the marginal cost of muffins? (b) Draw the demand and marginal cost on a diagram. (c) Determine the optimal number of muffins to sell in a single package. (d) What price should the firm charge for each park?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…Question 1 Sal's Streaming Company streams TV shows to subscribers in the US and Canada. Demand is Qus 50 (1/3)Pus - QCA 80 (2/3)P CA = - where Q's are in thousands of subscriptions per year and P's are the subscription prices per year. The cost of providing Q units of service is given by TC = 1000 + 30Q, where Q = Qus+ QCA (a) What are the profit-maximizing prices and quantities for the US and Canadian markets? (b) As a consequence of a new VPN service that Facebook has developed, subscribers in Canada are now able to get the US streams and vice versa, so Sal can charge only a single price. What is the profit-maximizing single price that he should charge? (c) In which situation is Sal better off? In terms of consumers' surplus which situation do people in Canada prefer and which do people in the US prefer? Why?
- |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.)(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem зShakti Inc. has been granted a patent for its arnica toothache balm. The table to the right shows the demand and the total cost schedule for the firm. What is Shakti's profit minus maximizingoutput? A. 4 units B. 6 units C. 7 units D. 5 units Price per dose (Dollars) Quantity Demanded (Dose) Total Cost of Production (Dollars) $80 0 $80 72 1 82 64 2 88 56 3 100 48 4 124 40 5 164 32 6 208 24 7 268 16 8 340
- Help meSuposse 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)What is the in-state and the out of state elasticity? Give your answer to two decimals.
- A company produces a special new type of TV The company has fixed costs of 5497,000, and it costs $1100 to produce each TV The company projects that if it charges a price of $2200 for the TV, it will be able to sell 800 TVs. If the company wants to sell 850 TVs, however, it must lower the price to $1900. Assume a linear demand. What price should the company charge to earn a profit of $883,0007 It would need to charge $ (Round answer to nearest dollar. If more than one answer, separate with a comma)2. You are the Southeastern Michigan regional manager at Coca-Cola, responsible forproduction and pricing in the Metro Detroit area. Your primary competitor is Pepsi. The marketresearch team at Coca-Cola is thinking about launching a new product, Orange Vanilla Coke, toboost the brand. The cost function to produce a 12-pack of 12 fl. oz. cans of Orange VanillaCoke is C(qcoke) = 0.25qcoke and the market research team has estimated inverse market demandfor a 12-pack of this new “pop” in Southeastern Michigan to be P = 10.25 – 0.00025Q. a. Assuming Pepsi decides not to produce a similar product, allowing Coca-Cola to maintainmonopoly power in the market for orange vanilla cola, what price and quantity will youchoose to maximize profit? How much profit does Coca-Cola earn?b. What price and quantity you would choose to maximize profit if Pepsi spies discover yourproduct before launch, allowing Pepsi to produce and launch an identical product at the sametime. For your answer, assume the cost…(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?