BUAD 311 Operations Management
Homework 3: Linear Programming
1.
Let X be the number of standard cookies
Let Y be the number of deluxe cookies
a)
max. 3X + 4Y
s.t.
X + Y <= 30
5X + 10Y <= 200
X >= 0
Y >= 0
b)
The feasible region is the area shaded in the graph.
c)
5X + 5Y = 150
5X + 10Y = 200
5Y = 50
Y = 10
X = 20
Revenue is maximized at the intersection of the two curves drawn on the graph,
which is $100 and the product mix is 20 standard cookies and 10 deluxe cookies.
The choice is unique because that point is the extreme point of the feasible region
and any point beyond that would not be in the feasible region.
2.
It does not change the optimal mix found in 1© because the changes made only
changes the objective function and not the constraints. Given the same
constraints, the graph drawn would be the same and therefore, the extreme point
Y
30
40
30
X
20
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of the feasible solution giving the optimal product mix would not change.
However, the objective value would change and her revenue will increase from
$100 to $137.50.
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 Spring '07
 Vaitsos
 Management, Operations Research, Optimization, Mathematical optimization, Constraint, Burning River, Expansion Draft Burning

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