A firm has an inverse demand function P = 26 - 4Q. It has Fixed Costs of 90, and it costs an additional 2 for each unit of output produced. The profit function is, therefore: - 4Q2 +26Q - ⁹0/Q +3 -34 - 6Q - 4Q²+24Q - 90 -4Q² +28Q-90 -4Q-⁹0/+24
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- AMCO is a firm producing tables in Spain. It has a fixed cost of 100$ and a cost per unit of production of 2$. The demand function for a table is given by: P = 60 - 4Q 1. Find the equations of TR and TC. 2. Write down the equation of the profit. 3. Find Qwhen TR = 0 (x-intercept/roots). 4. Find Qwhen TR is a maximum. 5. Deduce the maximum total revenue (TR max).A local microbrewery has total costs of production given by the equation TC=500+10q+5q2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) Write the equations showing the brewery's average variable cost.A manufacturer of mountain bikes has the following marginal cost function: C′(q)=700/0.5q+2 where qq is the quantity of bicycles produced. When calculating the marginal revenue and marginal profit in this problem, use the approach given for the marginal cost and marginal revenue in the discussions in your textbook. a) If the fixed cost in producing the bicycles is $3200, find the total cost to produce 35 bicycles.Answer: $ b) If the bikes are sold for $250 each, what is the profit (or loss) on the first 35 bikes?Answer: $ c) What is the marginal profit on bike number 36?Answer: $
- 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) = 50+ 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = 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. $ profit $ marginal revenue $ marginal profit $ revenue Interpret the results. The approximate |---Select--- per additional copy per additional copy Interpret your answer. from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies 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.A local microbrewery has total costs of production given by the equation TC=500+10q+5q2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 – (1/2)*P. a) Write the equations showing the brewery's average fixed costs .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) = 70 + 0.10x + 0.001x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = 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 $ profit $ marginal revenue $ per additional copy marginal profit $ per additional copy Interpret the results. The approximate from the sale of the 501st copy is $ . (c) For which value of x is the marginal profit zero?x = copiesInterpret 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.
- 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.A major software developer has estimated the demand for its new personal finance software package to be Q=1,000,000P-2 while the total cost of the package is C = 10,000+ 25Q. If this firm wishes to maximize profit, what percentage markup should it place on this product where percentage markup is defined as 100*(sale price - marginal cost)/marginal cost? 4. a. b. C. d. e. ANS: 90% 100% 20% 40% 250%(a) Teddy Jis a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (1) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.
- 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) = 80+ 0.10x + 0.001x² dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.] R'(x) = 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 profit marginal revenue marginal profit Interpret the results. The approximate loss per additional copy per additional copy Interpret your answer. from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? X = copies The graph of the profit function is a parabola with a vertex at x = copies. so the profit is at a maximum when you produce and sell ITeddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750 ml size is q = 4000-250p and his total cost function is C (q) = 500 + 0.2q. Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750 ml bottles of dish washing liquidA 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