Question

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? 4x + h = 84 what is the objective equation? the volume is v = x^2h (c) express the quantity to be maximized as a function of x. v =

Explanation:

Step1: Isolate h from constraint

From $4x + h=84$, we get $h = 84 - 4x$.

Step2: Substitute h into volume formula

Substitute $h = 84 - 4x$ into $V=x^{2}h$. Then $V=x^{2}(84 - 4x)=84x^{2}-4x^{3}$.

Answer:

$84x^{2}-4x^{3}$