Question

Need Calculus help

In order to prototype a two dimensional game, you first need to create a cardboard mock-up. Since you’ll be creating several versions of this game, you want to save money. Therefore, you have to minimize the amount of cardboard used. The play area of the prototype must be 36 square inches.

the bottom 1.5 inches of the mock-up is reserved for buttons and controls and the right-hand 2 inches is reserved for information and statistics. What are the total dimensions of the mock-up such that the amount of cardboard used is minimized?

This is what I have
a. Primary equation Total Area (w + 2)( h + 1.5)
b. Secondary equation The play area w = 36/h
c. Function of one variable
A = (36/h + 2)(h + 1.5)
FOIL
36 + 54/h + 2h + 3
= 39 + 54/h + 2h
d. Feasible domain (0, 36) or (0, 18)

I my be off on the domain

need help with

d. Feasible domain

e. Graph of single variable vs. area

f. Final dimensions calculation through differentiation

g. Pseudocode of your solution

Answer 1

Seems like the feasible domain for the height is (0, +infinity) except that you already know you aren't interested in extremely tall play areas with almost no width.

Answer 2

It also looks like you have a clear function A = f(h) existing in the first quadrant. Might look something like: