Food taste vs. health. Is this an optimization problem?

Question

Consider restaurant menu choices: \begin{array}{c|c|c} \mathbf{Name} & \mathbf{Taste} & \mathbf{Health} \\ \hline \mathrm{Soup} & 7 & 6\\ \mathrm{Bread} & 8 & 3\\ \mathrm{Eggs} & 5 & 5\\ \mathrm{Fish} & 3 & 10\\ \mathrm{Chicken} & 5 & 8 \\ \mathrm{Steak} & 9 & 5\\ \mathrm{Candy} & 10 & 1\\ \mathrm{Cake} & 8 & 3\\ \hline \end{array}

Is there a way to extract the ideal food to eat? What kind of math can I do with this?

Is this related to basic optimization taught in Linear Algebra or Operations Research ?

Answer 1

Main question would be how do you understand what is the ideal food? With 2 given data categories, you can, e.g., say ideal is

• best tasting (in which case candy is best) or
• best health (in which case fish is best), or
• you design some sort of metric by which you can rank the foods, for example health per unit taste, in which case you divide the second number by the first and pick the one with the biggest ratio (and fish comes out best).

You can design more complex metrics, but everything comes down to what does ideal mean.

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UPDATE

For ideal = taste + health, just compute that for every line and pick the best one. The standard optimization methods from operations research would be a better fit if you were trying to construct some diet of these foods, maximizing the ideal diet parameters over some constraints.

Answer 2

It could be an optimisation problem, depending on how you define ideal. Following is a simple linear model: $$ \text{Benifit}(f) = \lambda T(f) + \beta H(f)$$ Where $f$ is a given food and $T(f)$ is the taste of food and $H(f)$ is the Health. $\lambda$ and $\beta$ depend on the trade-off between health and taste your definition of ideal allows. And the optimisation problem is the following: $$\arg \max_{f} \mathrm{Benefit(f)}$$