QS.1 - Integrate the following: 3x² ( 12x³ + 20 10.5 within the range 6 and 8. QS.2 - The marginal revenue of a firm is given by the following equation: MR(Q) = 20 + 14Q +13Q² Where, Q represents the quantity produced. Also given, the total revenue of the firm, when they produce 5 units of output, is 50, i.e., TR(5) = 50. - Calculate the firm's total revenue function. What is the value of the constant term in the total revenue function? (Answer in two decimal places. Be careful about the sign) - Calculate the total revenue of the firm when the firm produces 7 units of output.
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- 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 2920 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-xdA company manufactures a smartphones which sell for $r and y portable speakers which sell for $s. The weekly demand and cost equations are as follows: r=-3x+3y +327 S = x - y + 429 C(x, y) = 120 x + 130 y + 320 At a production level of 27 smartphones and 64 portable speakers, what is the marginal profit associated with selling smartphones? O a) $279 per smartphone O b) $501 per smartphone O c) $301 per smartphone O d) $69 per smartphone
- Suppose that a demand equation is given by q=1750-25p and the cost of producing q units is given by C(q) = 63,000-70q+0.02q2. Find the marginal profit for the following production levels. (a) 700 units (b) 1055 units (c) 1600 units (a) The marginal profit for a production level of 700 units is (Simplify your answer.)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 functionMarginal 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). $ 900
- The marginal cost, in dollars per unit, for a company's portable heater is C'(q) = 48 – 0.03q + 0.00002q? and the marginal revenue is R'(q) = 44 – 0.007q. Find the area A between the graphs of these functions for 0 R'(q) for 0 s9s 160. Round your answer to two decimal places.) A = Interpret your result. O The company's profit increased by this amount after producing and selling the 160th heater. O The company's profit increased by this amount after producing and selling the first 160 heaters. O The company's profit decreased by this amount after producing and selling the 160th heater. O The company's profit is this amount. O The company's profit decreased by this amount after producing and selling the first 160 heaters.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)Your college newspaper, The Collegiate Investigator, sells for 90¢ per copy. The cost of producing x copies of an edition is given by C(x) = 10 + 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) %3D P'(x) (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition. revenue 2$ profit 2$ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate loss from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies Interpret your answer. The graph of the profit function is a parabola with a vertex at x = , so the profit is at a maximum when you produce and sell copies.
- Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to beMC=q+35 MR=560+22q−q2Where q is the quantity produced and the firm’s break-even is 5 units per weekYou are Required to1. determine the total cost and the total revenue function in terms of q.2. estimate the output at which profit is maximize3. calculate the maximum profitA 62 metre length of rope is cut into pieces whose lengths are in arithmetic progressionwitha common difference of d metres. Given that the lengths of the shortest and thelongest pieces are 0.5 and 3.5 metres respectively, find d.(C) For a firm’s product, the demand function isp = 72 2 0.04qand the average cost function isc¯ =500q+ 30 At what level of output would profit be maximized?-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.