suppose that postal requirements specify that parcels must have length plus girth at most 84 inches…

suppose that postal requirements specify that parcels must have length plus girth at most 84 inches. consider the problem of finding the dimensions of the square - ended rectangular package of greatest volume that is mailable. each square end is labeled with x and the remaining dimension is labeled with h. (a) express the length plus the girth in terms of x and h. 4x + h (b) determine the objective and constraint equations. what is the constraint equation?

suppose that postal requirements specify that parcels must have length plus girth at most 84 inches. consider the problem of finding the dimensions of the square - ended rectangular package of greatest volume that is mailable. each square end is labeled with x and the remaining dimension is labeled with h. (a) express the length plus the girth in terms of x and h. 4x + h (b) determine the objective and constraint equations. what is the constraint equation?

Answer

Explanation:

Step1: Identify the constraint

The postal requirement states that length plus girth is at most 84 inches. Since length plus girth is (4x + h), the constraint equation is (4x+h\leq84). For finding the maximum - volume, we consider the equality case (4x + h=84), so (h = 84 - 4x).

Step2: Define the objective function

The volume (V) of a rectangular box with square base of side - length (x) and height (h) is (V=x\times x\times h=x^{2}h). Substitute (h = 84 - 4x) into the volume formula, we get (V(x)=x^{2}(84 - 4x)=84x^{2}-4x^{3}).

Answer:

The constraint equation is (4x + h=84)