A manufacturer can produce at most 90 units of a certain product each year . The demand equation for the product is p= q2-100q+1800 and the manufacturer's average cost function c=2/3q2-55q+12000/q Determine the profit maximizing output q and the corresponding maximum Profit . The profit maximizing output q is 60
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- The economic analysis division of Mapco Enterprises has estimated the demand function for its line of weed trimmers as QD=18,000+0.4N350PM+90Ps where N=numberofnewhomescompletedintheprimarymarketarea PM=priceoftheMapcotrimmerPS=priceofitscompetitorsSurefiretrimmer In 2010, 15,000 new homes are expected to be completed in the primary market area. Mapco plans to charge $50 for its trimmer. The Surefire trimmer is expected to sell for $55. What sales are forecasted for 2010 under these conditions? If its competitor cuts the price of the Surefire trimmer to $50, what effect will this have on Mapcos sales? What effect would a 30 percent reduction in the number of new homes completed have on Mapcos sales (ignore the impact of the price cut of the Surefire trimmer)?The profit function in dollars for a product is given -x^3+76x^2-380x-2800 where x is the number of units produced and sold. If break even occurs when 10 units are produced and sold find a quadratic factor of the profit function and find a number of units other than 10 that gives break even for the product.Given a linear supply function of the form QXs = 3,000 + 3PX - 2Pr - Pw, and assuming Pr = $1,000, Pw = $100, and PX=50, the PS is: (use commas: 30,000 instead of 30000)
- Q1. Game console manufacturing determines that in order to sell Q units, the price per unit (in dollar) must decreased by the linear demand (the demand function) P(Q)= 800- 0.3Q($/device) The manufacturer also determine that the cost depends on the volume of production and includes a fixed part 500,000($) and a variable part 500Q , that is C(Q)= 500000+ 500Q What price per unit must be charged to get the maximum profit?Worldwide annual sales of a device in 2012–2013 were approximately q = −6p + 3,040 million units at a selling price of $p per unit. Assume a manufacturing cost of $40 per unit. [HINT: Recall that Profit = Revenue − Cost.] Find the function P for annual profit, in millions of dollars and in terms of p only, subject to any constraints. P(p) = ____ Find P′(p). P′(p) = ____ What selling price (in dollars) would have resulted in the largest annual profit? (Round your answer to two decimal places.) p = $____ What would have been the resulting annual profit (in millions of dollars)? (Round your answer to the nearest whole number.) $ ____ millionJim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a straight commission of $1,000 per house sold. Over the past year, Jim has sold up to 6 homes in a month. Write down the month salary payoff table for Jim.
- A manufacturing firm maintains one assembly line to produce signal generators. Weekly demand for the generators is 35 units, and the line operates for 7 h/d, 5 d/wk. What is the maximum production time per unit required of the line in order to meet demand?Your client, InsureCorp, is an insurance company considering launching an ‘income insurance’ product in the island nation of Autarka. Income insurance is a product that fully insures a household against changes in income caused by a major injury or illness. At present, no businesses are selling income insurance products in Autarka. Initial market research suggests that there are 10,000 households in Autarka interested in purchasing income insurance. Your client expects that the fixed cost of launching the income insurance product will be $20,000,000 per year, and that each policy issued to a customer will cost the company an additional $1,500 in sales commissions. What is the maximum price the company can charge a household for an income insurance policy? What is the expected profit (or loss) for the company if it becomes a monopoly provider of income insurance? Is there a risk that rival insurance companies will also enter the market, selling identical income insurance products? If…Demand for a company’s product is given by the following equation: Q=1000-0.5P. You are also given that its total cost function TC=100+1000Q. Compute the profit maximizing price and quantity B. A firm earns an accounting profit of K150, 000 per year in project A. The firm could earn K150, 000 and K120, 000 in investments B and C, respectively. How much economic profit is the firm earning assuming the three projects are mutually exclusive?
- Ptarmigan Company produces two products. Product A has a contribution margin of $84.00 and requires 8 machine hours. Product B has a contribution margin of $133.90 and requires 13 machine hours. Determine the most profitable product assuming the machine hours are the constraint. If required, round your answers to two decimal places.Let 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is −3.0. The marginal cost of producing the product is constant at $150, while average total cost at current production levels is $215. Determine your optimal per unit price if: Instructions: Enter your responses rounded to two decimal places.