Calc

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a fast food place sells 425 large orders of fries per week at price $2.75 each. A market survey indicates that for each $0.10 decrease, sales will increase by 20 orders of fires

a) Determine the ,marginal revenue function

b) With what price with marginal revenue be equal to zero, interpret this value

  • Calc -

    let the number of 10 cent decreases by n

    then price of fries = 2.75-.1n
    number sold = 425 + 20n
    revenue = (2.75-.1n)(425+20n)
    d(revenue)/dx = (2.75-.1)(20) + (425+20n)(-.1) = 0 for a max of revenue
    55 - 2n - 42.5 - 2n = 0
    -4n = -12.5
    n = 3.125

    I would assume that the decreases would be complete multiples of 10 cents, so there should be 3 decreases or a 30 cent decrease

    when n = 3
    they will have a price of 2.45
    and they will sell 485

    revenue = 2.45(485) = 1188.25

    check:
    if n=2
    revenue = 2.55(465) = 1185.75 , which is lower
    if n=4
    revenue = 2.35(505 = 1186.75 , which is also lower than the n=3 value

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