The cost function for q units of a certain item is C(q) = 106q + 104. The revenue function for the same item is R(q) = 106q + 47q/In(q) Find the marginal cost. Find the profit function. Find the profit from one more unit sold when 8 units are sold.
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- Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)Marginal Revenue for an Apartment Complex Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting x apartments is represented by the following function. P(x) = -6x² + 1620x - 36000 (a) What is the actual profit realized from renting the 61st unit, assuming that 60 units have already been rented? $ 40,434 X (b) Compute the marginal profit when x = 60 and compare your results with that obtained in part (a). $ 900Your 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.
- 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?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 function920 it bait of 289301 Sindspis ON SEU pilkupeni A30S AO +32 monulo2 An economist for a sporting goods company estimates the revenue and Cost functions for the production of a new snowboard. These Functions are R(x) = -x ² +10x and ((x) = 4x+5, respectively, where x is the number of Snowboard's produced in thousands. The average profit is defined by the function AP(x) = P(x), where pox) is the profit function & Determine the production levels that make AP(x) > 0 P-xd
- The revenue for a product is R(x) = - 0.004x2 + 21x – 6200 and the cost is C(x) = 0.02x + 38 for x units produced and sold. 1. Find the marginal profit for 2800 units. 2. Should output be increased or decreased to generate a higher profit?Question 1 A computer retailing company specializes in the sale of jump drives to community college students The demand function for jump drives is p=2x- +10=1000 dollars For the samne company the average cost function is given as. 2+36v-1600 - dollars Where pis the price n dollars and x represents units ofiourput. Determine the revenue function Determine the cost funetion Determine the profit function Find the price and output that will maximıze profir, Find the maximum profit 11 111) Iv) Ouestio n 2-n 5. A company estimates that the total revenue, R, in dollars, received from the sale of q items is R(q) = 3000+ln(2000+q²) and the marginal cost is MC(q) = 0.05q² +1.6q – 50. Calculate and interpret the marginal profit at q = = 10.
- 1. It costs $25,000 to build 30 refrigerators. It costs $30,000 to build 40 refrigerators. Assuming that the cost function is linear, find the cost function C(x) where x is the number of refrigerators built. If each refrigerator sells for $1500, find the revenue function, profit function, and break-even point.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) Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q.(i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J′s profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing whenhe produces 5 hundred, 750ml bottles of dishwashing liquid.(iv) How many 750ml bottles of dishwashing liquid should Teddy J produceper month if he wishes to maximize his profits.(b) A firm has an average cost functionA(q) =125q+q216 − 4.where q is the firm′s output.(i) Determine the level of output for average costs are minimum.(ii) Hence determine the range of values for which average costs are decreasing.(iii) What part of the decreasing range is practically feasible?(iv) Write an equation for the total cost function.(v) Hence calculate the level of output for which total costs are minimum.