suppose that postal requirements specify that parcels must have length plus girth at most 104 inches…

suppose that postal requirements specify that parcels must have length plus girth at most 104 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 = 104 what is the objective equation? the volume is v = x^2h (c) express the quantity to be maximized as a function of x. v =

suppose that postal requirements specify that parcels must have length plus girth at most 104 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 = 104 what is the objective equation? the volume is v = x^2h (c) express the quantity to be maximized as a function of x. v =

Answer

Explanation:

Step1: Isolate h from the constraint

Given $4x + h=104$, we get $h = 104 - 4x$.

Step2: Substitute h into the volume formula

The volume formula is $V=x^{2}h$. Substitute $h = 104 - 4x$ into it, we have $V=x^{2}(104 - 4x)=104x^{2}-4x^{3}$.

Answer:

$104x^{2}-4x^{3}$