Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x)=0.005x³ +0.02x2 +0.5x Currently, Pierce sells 90 lawn chairs daily a) What is the current daily revenue? b) How much would revenue increase if 95 lawn chairs were sold each day? c) What is the marginal revenue when 90 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(91), R(92), and R(93) a) The current revenue is $ b) The revenue would increase by $ (Round to the nearest cent.) c) The marginal revenue is $ when 90 lawn chairs are sold daily d) R(91) $ R(92) $ R(93) $
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- Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)A particular computing company finds that its weekly profit, in dollars, from the production and sale of x laptop computers is P(x) = -0.006x³ -0.3x² +600x-800. Currently the company builds and sells 7 laptops weekly a) What is the current weekly profit? b) How much profit would be lost if production and sales dropped to 6 laptops weekly? c) What is the marginal profit when x = 7? d) Use the answer from part (a) and (c) to estimate the profit resulting from the production and sale of 8 laptops weekly a) The current weekly profit is $ (Round to the nearest cent as needed) b) The decrease in profit is $ (Round to the nearest cent as needed.) c) The marginal profit when x=7 is $ (Round to the nearest cent as needed) CLOT d) The profit resulting from the production and sale of 8 laptops weekly is approximately $ (Round to the nearest cent as needed)A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit function
- Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.006x³ +0.02x² +0.6x. Currently, Pierce sells 90 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 95 lawn chairs were sold each day? c) What is the marginal revenue when 90 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(91), R(92), and R(93). (…) a) The current revenue is $ b) The revenue would increase by $. (Round to the nearest cent.) c) The marginal revenue is $when 90 lawn chairs are sold daily. d) R(91) ≈ $ R(92) $ R(93) $14.The demand function for a new product is p(x) = - 2x + 7 , where p is the selling price of the product and x is the number sold in thousands. The cost function is C(x) = x + 2 . a) Determine an equation for the profit, in standard form and in function notation. b) How many units must be sold for the company to break even?2) The owner of a restaurant that you are thinking of purchasing, tells you for x customers per week the weekly cost and revenue in dollars is C(x) = 15000+2x and R(x) = 500x-3x² a) Find the profit function P(x) b) Find the break-even quantities rounding properly to a whole number. (Hint: Use the Quadratic formula) c) Why is the minimum break-even quantity important?
- The market for smart thermostats has grown increasingly competitive. Producers of smart thermostats all rely on the same technology and face the same costs. The cost function for a smart thermostat producer is given by the following function: c(y)=-10y+2003 where y stands for the number of smart thermostats produced and sold in a month. 2nd attempt Suppose the market demand for smart thermostats in any month is given by QD = 305 - p. In the long-run equilibrium, we would expect to find firms in the industry. See HintYour college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 60 + 0.10x + 0.001x² dollars. (a) Calculate the marginal profit function, in dollars per copy. P'(x) = (b) Compute the marginal profit, if you have produced and sold 500 copies of the latest edition. When you produce and sell 500 copies, the marginal profit is dollars per copy. Interpret the results: The approximate loss from the production and sale of the 501st сорy is dollars.. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.
- 2 The company Shirts Galore has figured its total cost of producing and sclling x units of T-shirts per month is given by the equation C(x) = 120 +2.5x-0.0002r. a) Write a rational function to represent the average cost of producing and selling a shirt. b) If the production level is 1200 shirts per month, find the average cost of producing and selling a shirt. c) If the shirts are sold for $7.98 a shirt, what is the profit realized on producing and selling 1200 shirts per month? d) What price must be charged when selling the shirts for a profit of $7368 to bc made on 1200 shirts in one month? * A large company is considering changingA 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…E Let the demand function for a product be given by the function D(q) = -1.65g + 270, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $4, 000 and variable costs are $3 per item produced. If 96 items are produced and sold, find the following: A) The total revenue from selling 96 items (to the nearest penny). Answer: $ B) The total costs to produce 96 items (to the nearest penny). Answer: $ C) The total profits to produce 96 items (to the nearest penny. Profits may or may not be negative.). Answer: $ Question Help: C ME PE Video 66°F Mostly cloudy