11th grade math

posted by .

A farmer wants to fence in 60 000m^2 of land in a rectangular field along a straight road. The fencing that he plans to use along the road is $10 per meter and the fencing that he plans to use for the other three sides costs $5 per meter.
a) How much of each type of fence should he buy to keep his expanses to a minimum?
b) What is the minimum expanse?

  • 11th grade math -

    width of field --- x
    length of field --- y , with y as the distance along the road

    xy = 60000
    y = 60000/x

    cost = 5(2x+y) + 10y
    = 10x = 15y
    = 10x + 15(60000/x)
    = 10x + 900000/x

    d(cost)/dx = 10 - 900000/x^2 = 0 for a min of cost
    10x^2 = 900000
    x^2 = 90000
    x = √90000 = 300
    then y = 60000/300 = 200

    so the field should be 200 m by 300 m , with the 200 metres along the road

    minimum expense = 10x+ 15y = 3000 + 3000 = $6000

  • 11th grade math -

    There were 27 students who completed a survey. There were 14 boys and 13 girls. One survey was picked at random. To the nearest hundredth, what is the probability it was completed by a girl?

  • 11th grade math -

    13/27

  • 11th grade math -

    read3books4minits. Idonotnoaboutfillchrips.butmabesomere
    time.readyourbooks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What …
  2. Calc

    A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What …
  3. Calc

    A farmer wishes to enclose a rectangular pen with area 100 square feet next to a road. The fence along the road is to be reinforced and costs $34 per foot. Fencing that coast $16 per foot can be used for the other three sides. What …
  4. Math

    A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed?
  5. Pre-Calculas 11

    a farmer wants to build two pens (one for cows, the other for horses) on land by a straight road. There is already a fence along the road and the farmer has 800m of fencing to build his fence to enclose the pens and separate them as …
  6. math

    The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at $50 per meter. If the total cost of fencing is $12,000, what are …
  7. algebra

    The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along its two lengths and one width is to be done at $50 per meter. If the total cost of fencing is $12,000, what are …
  8. College Cal 1

    A farmer wants to fence off a rectangular field of area 15000 square feet using barbed wire fencing. SInce the opposite of the road is a corn-field, he wants a two-strand fence along the road, and one strand on each of the other three …
  9. Algebra

    Word Problems: 1. A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. If he needs no fence along the river, what are the dimensions of the field that he can fence with the largest …
  10. Math1210

    The perimeter of a rectangular field is 300 meters. This field is to be fenced along three sides only. The fencing along it's two lengths and one-width is to be done at $50 per meter. If the total cost of fencing is $12000, what are …

More Similar Questions