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 Calculus Calculus Math Forum

 June 5th, 2015, 12:47 AM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Calculus in Economics A company is planning to manufacture and market a new headphone set. After conducting extensive market surveys, the research department provides the following estimates: Marginal costs function: $c'(x)=20+0.2x$ where $x$ is the quantity sold. Fixed cost:500 Demand function is linear :At the price of $78$, 30 units were sold. At the price of $58$,$50$ units were sold. Find the following a) Assume that the relationship between price $p$ and demand $x$ is linear . Express $p$ as a function of $x$. b)Find the total cost function c)Find the profit function d)The level of production in which profit is maximized. e) The maximum profit, price per unit, total revenue and total cost when profit is maximized. f) Find the change in total profit when production level increases from 50 units to 60 units. Interpret your results. My attempt, a) $p=mx+b$ $m=\frac{50-78}{58-30}=-1$ $p=-x+b$ $50=-58+b$ So, $p=-x+108$ b)Total cost function$=\int 20+0.2xdx$ $20x+\frac{0.2x^2}{2}+500=0.1x^2+20x+500$ c)$P(x)=xp(x)-c(x)=x(-x+108)-(0.1x^2+20x+500)$ $P(x)=-1.1x^2+88x-500$ d)$\frac{dP}{dx}=0$ $\frac{d}{dx}(-1.1x^2+88x-500)=0$ $88-2.2x=0$ $x=40$ Am I correct for my attempts? How to proceed for e) ? Can anyone give me some tips for me? Thanks Tags calculus, economics Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post questioner1 Calculus 8 December 23rd, 2014 10:35 PM frazza999 Economics 0 June 14th, 2014 08:49 PM cyborgwrath Advanced Statistics 0 January 6th, 2013 06:28 PM JJAtlanta New Users 4 August 8th, 2011 11:01 PM jadenb11 Economics 0 April 18th, 2011 04:57 PM

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