Problem:
Formulating a nonlinear program for profit maximization
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?