1. Complete the following optimization problems. (a) What is the maximum product of three numbers which add to 150, with one of the numbers being four times as large as another? (Hint: You can write three numbers as x, 4x, and y. (b) A rancher has 2400 feet of fencing in which to construct adjacent, equally sized rectangular pens (see figure below). What dimension should these pens have to maximize the total enclosed area in the two pens?

(c) The total linear length of a rectangular piece of luggage is the sum of its length, width, and height. TSA requires that the total linear length of checked baggage be at most 62 inches. What are the dimensions of a bag with maximum volume and total linear length 62 inches which is twice as long as it is wide?