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Formulating a nonlinear program for profit maximization

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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 = 4x1 + 2x2 + 0.003x12 + 0.004x22. 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. What is the equation associated with the constraint regarding the amount of time available for baking?

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Let x1 be the number of doughnuts produced andx2 be the number of muffins produced.

We want to maximize profit=4x1 + 2x2 + 0.003x1^2 + 0.004x2^2

Subject to ...

Solution Summary

The solution gives detailed steps on setting up a nonlinear programming model. Each equation is written based on each given statement.

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Nutrient Feed 1 Feed 2 Feed 3 Minimum Daily Requirements
A 2 3 7 950
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C 5 3 0 900
D 0.5 0.5 1 230
Cost 4.0 3.5 9.6

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Machining, h Polishing, h Assembling, h
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Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
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Orange Juice, % Grapefruit Juice, % Cranberry Juice, % Supply,
gal Cost,
$ / gal
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Cost, $1000 145 92 70 70 84 14 47

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