Math

posted by .

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 96 in. Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent via priority mail. Hint: The length plus the girth is 4x + h (see the figure below).

  • Math -

    well, we know

    4x+h = 96, so h=96-4x
    v = hx^2
    = x^2(96-4x)
    = 96x^2 - 4x^3
    = 4(24x^2 - x^3)

    dv/dx = 4(48x - 3x^2)
    = 12x(16 - x)

    dv/dx = 0 when x = 0 or 16
    so, h = 96-4*16 = 32

    So, if the package is 16x16x32
    v = 8192 in^3

    Now, technically, 4x+h <= 96, but it should be clear that max volume occurs when 4x+h is as large as possible.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calc

    A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 120 inches. a. Show that the volume of the package is V(x)= 4xsquared(30-x) b. Use your graphing …
  2. CALCULUS

    Postal regulations specify that a package sent by priority mail may have a combined length and girth of no more than 129 in. Find the dimensions of a cylindrical package with the greatest volume that may be sent by priority mail. Hint: …
  3. Math

    Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 144 in. Find the dimensions of a rectangular package that has a square cross section and largest volume that may be …
  4. Math

    Postal regulations specify that a package sent by priority mail may have a combined length and girth of no more than 129 in. Find the dimensions of a cylindrical package with the greatest volume that may be sent by priority mail. Hint: …
  5. Algebra 2

    A package with square ends has combined length and girth(girth is perimeter of a cross section) of 120 in. The surface area of the entire package is 3600 sq. in. Determine the dimensions of the package. s in. * s in.* l in. One solution …
  6. Trig

    The postal service places a limit of 84 inches on the combined lenght and girth (distance around) of a package to be sen parcel post. What Dimensions of a rectangular box with square cross-section will contain the largest volume that …
  7. CALCULUS

    1. A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent. (Assume the cross …
  8. Math Calculus

    Postal regulations specify that a package sent by certain shipping methods may have a combined length and girth of no more than 99 inches. Find the dimensions of a CYLINDRICAL package with the greatest volume that may be sent by this …
  9. Calc

    A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 90 inches (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume …
  10. calc

    1.A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window find the dimensions of a Norman window of maximum area when the total permeter is 16ft. 2. A rectangle is bounded by the x axis …

More Similar Questions