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Question 1
50 out of 50 points
A bakery produces muffins and doughnuts. Let x1 be the
number of doughnuts produced and x2 be the number of muffins produced.
The profit function for the bakery is expressed by the
following equation: profit = 4×1 + 2×2 + 0.3×12 + 0.4×22.
The bakery has the capacity to produce 800 units of muffins
and doughnuts combined and it takes 30 minutes to produce 100 muffins and 20
minutes to produce 100 doughnuts. There is a total of 4 hours available for
baking time. There must be at least 200 units of muffins and at least 200 units
of doughnuts produced. Formulate a nonlinear program representing the profit
maximization problem for the bakery.
Your response should be at least 200 words in length.
Question 2
50 out of 50 points
Classify the following problems as to whether they are
pure-integer, mixed-integer, zero-one, goal, or nonlinear programming problems.
Maximize Z = 5 X1 + 6 X1 X2 + 2 X2
Subject to: 3 X1 + 2 X2 ? 6
X1 + X2 ? 8
X1, X2 ? 0
Minimize Z = 8 X1 + 6 X2
Subject to: 4 X1 + 5 X2 ? 10
X1 + X2 ? 3
X1, X2 ? 0
X1, X2 = 0 or 1
Maximize Z = 10 X1 + 5 X2
Subject to: 8 X1 + 10 X2 = 10
4 X1 + 6 X2 ? 5
X1, X2 integer
Minimize Z = 8 X12 + 4 X1 X2 + 12 X22
Subject to: 6 X1 + X2 ? 50
X1 + X2 ? 40
Your response should be at least 200 words in length.
