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 %3D 10.
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- 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) = 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.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)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?
- 11.2 The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.01x2. (a) Find the marginal cost function C'(x). HINT [See Example 1.] C'(x) = Use it to estimate how fast the cost is increasing when x = 4. thousand dollars per television commercialCompare this with the exact cost of airing the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ . Thus, there is a difference of $ . (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) = thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.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)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.
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