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The publisher of a magazine that has a circulation of 80,000 and sells for 1.6 a copy decides to raise the price due to distribution costs. By surveying the readers the publisher finds that the magazine will lose 10,000 readers for every .4 increase in price. What price per copy maximizes the income?

  • pre calc - ,

    its 2.4

  • pre calc - ,

    let the number of .4 increases be n
    so the number of circulation copies is 80,000-10,000n
    and the price per copy is 1.6 + .4n

    So income is =(1.6+.4n)(80000-10000n)
    d(income)éà/dn = 16000-8000n = 0 for a max income
    n=2, so there are 2 increases of .4, for a final price of 1.6 + .8 = 2.4 as Julie stated above

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