diet - documentation

• Set F:

  Foods. \(\mathcal{F}\)

  Properties: Dimen=1, Domain=None, Ordered=False, Bounds=None

• Set N:

  Nutrients. \(\mathcal{N}\)

  Properties: Dimen=1, Domain=None, Ordered=False, Bounds=None

• Param cost:

  Cost of each food. \(c_f \geq 0\)

  Properties: Index=F, Domain=NonNegativeReals, Default=None, Mutable=False

• Param content:

  Amount of nutrient in each food. \(a_{f,n} \geq 0\)

  Properties: Index=content_index, Domain=NonNegativeReals, Default=None, Mutable=False

• Param min_intake:

  Lower bound on each nutrient. \(y^{min}_n\)

  Properties: Index=N, Domain=NonNegativeReals, Default=0.0, Mutable=False

• Param max_intake:

  Upper bound on each nutrient. \(y^{max}_n\)

  Properties: Index=N, Domain=NonNegativeReals, Default=inf, Mutable=False

• Param volume:

  Volume per serving of food. \(v_f\)

  Properties: Index=F, Domain=PositiveReals, Default=None, Mutable=False

• Param max_volume:

  Maximum volume of food consumed. \(v^{max}\)

  Properties: Index=None, Domain=PositiveReals, Default=None, Mutable=False

• Var x:

  Number of servings consumed of each food. \(x_f \geq 0\)

  Properties: Index=F

• Expression total_volume:

  Total volume of food consumed.

  \[v^{tot} = \sum_{f \in \mathcal{F}} v_f \cdot x_f\]

  Properties: Index=None

• Expression intake:

  Total intake of each nutrient.

  \[y_n = \sum_{f \in \mathcal{F}} \alpha_{f,n} \cdot x_f\]

  Properties: Index=N

• Objective minimize_total_cost:

  Minimize the cost of food that is consumed.

  \[\min_{x} \sum_{f \in \mathcal{F}} c_f \cdot x_f\]

  Properties: Index=None

• Constraint nutrient_limit:

  Enforce upper and lower bounds on intake of each nutrient.

  \[y^{min}_n \leq y_n \leq y^{max}_n\]

  Properties: Index=N

• Constraint volume_limit:

  Limit the volume of food consumed.

  \[v^{tot} \leq v^{max}\]

  Properties: Index=None