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Practice Questions: Linear Programming
1.
A steel manufacturer produces metal sheet in standard size of: width 11ft and
length 11ft. After the production, the plant can cut the sheet into the sizes a
customer may want. For example, it can cut a sheet into 2 pieces of 11ft*4ft
and one piece of 11ft*3ft. A customer comes and need 100 11ft*3ft, 200
11ft*4ft, and 300 11ft*5ft sheets. What is the smallest number of metal sheets
the company must produce to satisfy all the demand?
In order to produce the 100 11ft*3ft, 200 11ft*4ft, and 300 11ft*5ft sheets
from standard size 11ft*11ft sheet, the following cut pattern can be used.
a.
having 3 3ft one from one standard sheet
b. having 2 3ft one and 1 4ft one from one standard sheet
c.
having 1 3ft one and 2 4ft one from one standard sheet
d. having 2 3ft one and 1 5ft one from one standard sheet
e.
having 1 4ft one and 1 5ft one from one standard sheet
f.
having 2 5ft one from one standard sheet
Assume we use x_1, x_2, x_3, x_4, x_5, x_6 sheets for all the six cutting
pattern:
Objective
function: min x_1+x_2+x_3+x_4+x_5+x_6
Constraints:
3x_1+2x_2+x_3+2x_4>=100
x_2+2x_3+x_5>=200
x_4+x_5+2x_6>=300
The optimal solution is x_3=100, x_6=150, and all other xs equal to zero.
2.
The Sue All Law Firm handles two types of lawsuits: medical malpractice
suits against unscrupulous heart surgeons for performing unnecessary surgery,
and suits against hardworking math professors for failing students who do not
deserve to pass. Math professor lawsuits each require 6 personmonths of
preparation and the hiring of 5 expert witnesses, whereas medical lawsuits
each require 10 personmonths of preparation and the hiring of 3 expert
witnesses. The firm has a total of 30 personmonths to work with and feels
that it cannot afford to hire more than 15 expert witnesses. It makes an
average profit of $1 million per math professor sued and $5 million per heart
surgeon sued. How many of each type of lawsuit should it initiate in order to
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This note was uploaded on 03/09/2008 for the course BUAD 311 taught by Professor Vaitsos during the Fall '07 term at USC.
 Fall '07
 Vaitsos
 Management

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