Planning diet for the food and  Diamonds are forever

the formulation of the Mathematical Model underlying the solution to the question 1 (“Find the weekly diet that…”) is mandatory.

1-Start by including a low number of independent variables into your model and then proceed by increasing level of complexity

(by gradually increasing the number of decision variables you

introduce into your model);
2. At each step, compare the R square and Adjusted R square values of your resulting models.
3. Again, remember about the principle of parsimony (all other factors held equal, a better model is the one with fewer independent variables). Having said this Adjust R square should still be

your leading indicator.
4. If several instances of a new level of complexity

(say, the combination of three independent variables) does not produce a better Adjusted R square value, when compared to the best result

acquired at a lower level of complexity, then you may arrive at a conclusion that there is no point proceeding with adding new independent variables to the model.
This is where your search for the best fitted model will stop.

To reiterate, you certainly should not try all possible combinations of the six decision variables, but instead you should start by

considering a lower number of decision variables first and then progress towards increasing the complexity of your tentative regression models, continuously checking and updating your

Adjusted R Square values.