1. At midnight, you are 60 feet due north of Jonas. You run due east at ten feet per second. Jonas walks two feet per second due north. How many seconds after midnight is Jonas closest to you? What is the corresponding minimum distance separating you and Jonas?

Question

2. We need to build a building in the shape of a rectangular box with a capacity of 500,000 cubic feet. We require the length of the floor to be twice the width. The floor will cost $3 per square foot, the vertical walls will cost $4 per square foot, and the ceiling will cost $5 per square foot. To the nearest hundredth of a foot, what are the dimensions of the cheapest building that we can build? What is that building’s cost to the nearest dollar

Answer 1

the distance z between you and Jonas after t seconds is

z^2 = (60-2t)^2 + (10t)^2

For the box, we know
xyz = 500000
since y=2x,
2x^2z = 500000
x^2z = 250000
So, z = 250000/x^2

c(x) = (x)(2x)(3) + (6x)(250000/x^2)(4) + (x)(2x)(5)
= 16x^2 + 6000000/x

Now just do your minimum stuff.