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 February 21st, 2009, 11:54 AM #1 Newbie   Joined: Feb 2009 Posts: 2 Thanks: 0 Can somebody help solve this problems please A radio manufacturing firm has fixed cost of \$25.000 cost and variable cost of \$75.80 per radio. The radio sells for \$119.95. Write an expression for the profit function and find the number of radios that must be sold to break even. If money is invested at 9%, what is the effective annual rate if the investment is compounded a) quarterly? b) monthly? c) daily? d) countinuously? Last edited by skipjack; November 4th, 2016 at 08:04 AM.  February 26th, 2009, 02:16 AM #2 Global Moderator Joined: Dec 2006 Posts: 20,267 Thanks: 1958 Why are there three zeros in the fixed cost? Is it typed correctly? For the questions about interest rates, read this article.  February 26th, 2009, 10:11 AM #3 Senior Member Joined: Sep 2008 Posts: 116 Thanks: 0 Re: CAN SOMEBODY HELP SOLVE THIS PROBLEMS PLEASE If the zeros are correct and the fixed cost is just \$25.00, then you break even after the first radio because 119.95 - 25.000 - 75.80 = 19.15. Meaning you are making \$19.15 profit off the first radio sold. Now, assuming the fixed cost is supposed to be \$250.00, the formula becomes $119.95x= 250 + 75.8x$ $44.15x= 250$ $x= 5.66$ Because you can't sell .66 of a radio, round up to the nearest digit. So you need to sell 6 radios to start turning a profit. Total profit can be calculated with the function $f(x)= 44.15x - 250$ ************************************************** ************* ************************************************** ************* As for the second question, I could be wrong, but here it goes: Quarterly:$1 - (1 + \frac{0.09}{4})^4= 9.31%$ Monthly:$1 - (1 + \frac{0.09}{12})^{12}= 9.38%$ Daily: $1 - (1 + \frac{0.09}{365})^{365}= 9.42%$ Countinuously: not sure how to do this one though You could do it with calculus though like $\lim_{x \to \infty} 1 - (1 + \frac{0.09}{x})^x$ The limit should also equal $\infty$ I believe, again, don't quote me on it though... Last edited by skipjack; November 4th, 2016 at 08:04 AM.
 April 2nd, 2009, 02:05 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,267 Thanks: 1958 That limit is 1-e^0.09, but is the formula correct?

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