418 points I W In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in...

could you please help with these problems and give them with any explanations on how to start the problems and just working through them and how you know what to do

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1. 418 points I W In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in terms of their combined length, width and height(L+W+H). I am due to ﬂy on an airline that states "The sum of the length, the width and height of your item mustbe at most 65 inches". Suppose I want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, andthat I also want this box to have a square base. The questions we will answer using Optimization are: What dimensions should the box have, and whatwould be the resulting maximum volume? a. If the base of the box is a square whose sides have length x, and the height of the box is h (bothmeasured in inches), enter expressions for the volume of the box, V, and the sum of the length,width and height of the box in terms of x and h. wcvSumL+W+H—¢ b. Since the sum of the length, width and height must be less than or equal to 65 inches, and it isclearly best to choose this sum to equal 65 inches, write down the constraint equation. Rearrange the constraint equation to give the height of the box, h, in terms of the length of thebase, x h = vc. What is the objective function for this problem?Using the constraint equation, rewrite the objective function in terms of x alone v—« d. Differentiate V with respect to x, to ﬁnd the derivative dV/ dx.dVd1 = x