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1. After watching the two videos answer the following questions:
a. What are the underlying assumptions when we model a business problem as a linear
program?
b. What is the optimal solution to the custom molder problem? That is, how many cases of
6-oz glasses and 10-oz glasses should the molder produce? (The spreadsheet
GlassManufacturer_LP_Geometry in the Lecture 1 folder has the problem data)
a.) Following are the assumptions taken
 Proportionality: The effect of the decision variable is proportional to its coefficient.
 Additivity: The contribution to the objective by one decision variable is not associated with
the contribution by the other decision variable (contributions are independent)
 Divisibility: Each decision variable can take fractional values
 Data certainty: Coefficients for decision variables are constant, they are not random
variables.
b.) The values of X1 and X2 are as mentioned below.
VARS
PROFIT
X1
6.43
500
X2
4.29
450
Z
C1
C2
C3
6
10
1
5
20
0
60.000
150.000
6.429
<=
<=
<=
60
150
8
N1
N2
-1
0
0
-1
-6.429
-4.286
<=
<=
0
0
5142.86
c.) Consider the following feasible region to a linear programming problem, which is represented
by the grey shaded area. Which of the following can possibly be a unique optimal solution
(optimal for some objective function)? The candidate solution point is the red dot. Answer
Yes/No to each part.
i.
NO
ii.
NO
iii.
YES
iv.
YES
v. NO