1) A mainframe computer retailer is expanding by offering retailers in cities throughout the Midwest. Based upon recent operating experience, each mainframe sold will result in $10,000 in variable wholesale, service, and warranty costs. Also, each franchise will incur $500,000 per year in fixed over head costs. The retailer expects a typical franchise to face the following demand curve: P = 30,000 - Q Where P is the price in dollars and Q is the number of mainframes sold. What is the profit function for each franchise? п
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- Suppose you own a tax preparation services company, with fixed costs of $3,000/month and marginal costs of $25/appt.If the price is $60/appt, 500 appointments would be sold. If the price is $50/appt, 760appointments would be sold. a.)Use these figures to calculate the price elasticity of demand for your services. b.)Calculate the monthly profits and profit margins (profit/revenue) associated with the price of $60/appt and $50/appt. c.)Given these calculations, what price should you charge for your services, $50/apptor $60/appt? ExplainMultichoice company broadcasts to subscribers in Lusaka and Solwezi. The demand for each ofthese two groups are Qsz= 50 - (1/3) Ps and QUSK= 80 - (2/3) Pusk, where Q is in thousands ofsubscriptions per year and P is the subscription price per year. The cost of providing Q units.ofservice is given by C (Q) = 1000 + 30Q, where Q = Qsz + QusK. Assuming Multichoice is aMonopoly and can engage in third-price discrimination, then1. What is the profit-maximizing price and quantity in Solwezi Market?2. What is the profit-maximizing price and quantity in Lusaka Market?3. Suppose the Monopoly can only charge a single. What price should it charge and what isthe total quantity sold?Round off your final answer to whole #. A company produces and sells a consumer product and is able to control the demand by varying the selling price. The approximate relationship between price and demand is 2700 5,000 p=47 + -forD>1 D D² The company is seeking to maximize its profit. The fixed cost is $1,000 and the variable cost is $39 per unit. What is the number of units that should be produced and sold each month to maximize profit?
- 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…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)Sampson Ltd produces two products that can be produced on either of two machines. Each month, only 5o0 hours of time are available on each machine. The time required to produce each item by hour and machine is: Machine Machine Product 1 Product 2 3 4 Month Month 1 Month 2 Month 1 Demand Demand Price Price Product 1 100 160 $45 $65 $10 Product 2 120 110 $35 The demand and price point for each product that customers are willing to pay are above. The company goal is to maximize revenue from sales from the next two months. Based on the provided information, how many constraints does this problem have excluding the non-negativity constraints?
- Presently, APlus Transport and Big Movers are the only suppliers of services that haul heavy construction equipment between jobs within the Midwest. No other suppliers have the equipment necessary to perform the service. The market inverse demand for these hauling services is given below. P-4,030-40 where P is price per trip and Q is total number of trips per year. For simplicity, also assume that neither firm has fixed costs. From company records, you are given the following variable cost function for each firm: TVC,=300, TVC, - 800 a. Assume these two competitors operate as a two-firm Cournot duopoly. Find the reaction functions for each firm. b. Calculate the Cournot market equilibrium price-output solutions for each firm including their respective profits. c. Suppose Big Movers shuts down operations so that APlus now has a monopoly in this market. What is the price, quantity, and profits for APlus after this change? d. Summarize the results of your findings over the two possible…Hotel Del Luna has 10 rooms with a marginal cost of $20. During the high season, the demand equation is QH = 700- 2PH, where QH is the number of rooms and PH is the room %3D rate per night during the high season. During the low season, the demand equation is Q1, = 420 PL, where QL, is the number of rooms and P, is the room rate per night during the low season. What is the profit-maximizing room rates during the high season (PH)? O PH= $700. %3D O PH = $420. PH = $345. %3D PH = $300. None of the above.A company has established that the relationship between the price for one of its products is approximately p = 88.5 – 0.08D0.75 In addition there is a fixed cost of $45,000 per year and the variable cost to manufacture the product is $45 per unit. What level of demand maximizes the total revenue? Ans. is Blank 1 What level of demand maximizes the total profit for this product? Ans. is Blank 2 Blank 1 Add your answer Blank 2 Add your answer
- The Poster Bed Company believes that its industry can best be classified as monopolistically competitive. An analysis of the demand for its canopy bed has resulted in the following estimated demand function for the bed:P = 1760 - 12QThe cost analysis department has estimated the total cost function for the poster bed asTC = (1/3)Q3 - 15Q2 + 5Q + 24,000a. Calculate the level of output that should be produced to maximize short-run profits. b. What price should be charged? c. Compute total profits at this price-output level. d. Compute the point price elasticity of demand at the profit-maximizing level of output. e. What level of fixed costs is the firm experiencing on its bed production? f. What is the impact of a $5,000 increase in the level of fixed costs on the price charged, output produced, and profit generated?Systems applicationSolve and analyze the following problems. Make sure all the steps are properly justified. Correctly use mathematical notation or terminology. Interpret the solution in the context of the problem.Suppose the supply and demand equations for printed shirts for a graduating class are given byp = 0.7q + 3p = -1.7q +15where p is the price in dollars and q is the quantity in hundreds.Determine supply and demand if the shirts cost $ 9.00. Analyze and discuss the stability of the shirt market at this price level. Prepare the graph of the two equations in the same coordinate system and identify the equilibrium point, the supply curve, and the demand curve.Bavarian Crystal Works designs and produces crystal wine decanters for export to international markets. The marketing manager of Bavarian Crystal Works estimates the demand curve for each month to be: P=1,000-0.0025Q where Q is the number of wine decanters produced annually. Bavarian Crystal Works also pays a lease for its factory and equipment every month in the amount of $1,000,000. Finally, the cost to produce each wine decanter is $200. What is the marginal revenue at 40,000 units? If Bavarian Crystals is currently producing 40,000 units would you recommend they increase their production?