After setting up the still described in the previous problem, the engineering st
ID: 3144093 • Letter: A
Question
After setting up the still described in the previous problem, the engineering students felt that a celebration was in order. Knowing that their own booze had been made in a bathtub, they decided that going out to a local bar might be a better idea. As luck would have it, the bar was holding a BYOM (Bring Your Own Mug) night. Wanting to avoid having students bring in 5 gallon buckets for mugs, the bar posted the following restrictions: What a deal, they thought. We can design our own mugs to hold as much beer as possible! What is the optimum design? (a) Formulate the problem. (With precision, as engineering students are wont to do.) (b) Solve the problem utilizing the methods of Chapter 4 (c) Verify your solution graphically (d) Which constraints (if any) are active?Explanation / Answer
Ans(a):
5<=R<=20
H<=20
surface area A<=900 cm^2 (ignore the bottom surface area of mug and handle)
Surface area of the mug is cylindrical so area is given by
A=2 pi R H
then 2 pi R H<=900 (using A=2 pi R H)
or R H<=900/(2pi)
Volume V= pi R^2 H
Then the LPP formulation will be:
Maximize V=pi R^2 H
subject to constraints:
5<=R
R<=20
H<=20
R H<=900/(2pi)
H>0 (non negativity constraint)
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Methods of Chapter 4 are not listed so can't proceed for part b).