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Calculus Help Questions?

Mathematics
footballstarlhsn asked:


1. A farmer wants to create a 300 square foot rectangular grazing pen for his sheep. The barn will form one side of the pen, but he will will have to buy fencing for the other three sides. Find the minimum length of fencing that will be required.

2. A baseball stadium holds 20,000 people. At a selling price of $15 per ticket, the stadium fills to capacity. For each $1 in ticket price, 500 fewer tickers are sold.

a.Find the ticket price that maximizes revenue from ticket sales.
b. Find the maximum possible revenue from ticket sales in the stadium.

3. The cost to produce q goods is given by C(q)=2000+50q+2q^(2) for 0 a. Find the average cost if 70 items are sold.
b. Find the minimum average cost.
c. Find the maximum profit if each item is sold for $350.

Harvey

1 Comment

1 Comment

  1. gregschaeffer  •  Aug 8, 2009 @2:49 am

    Ana

    1) 300 = LW (so L=300/W)
    P = 2W + L = 2W + 300/W

    We have the perimeter in terms of W only. Take P’ and find when it equals 0.

    P’ = 0 = 2 + 300 (-1 / W^2)
    2 = 300 / W^2
    W^2 = 150
    W = sqrt(150)

    Total length = P = 2W + 300/W =
    2*sqrt(150) + 300 / sqrt(150) =
    48.9897949 feet of fence

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