Let us first solve the following subproblem: how many dollars must we pay to buy ~G~ units of some ingredient?

This subproblem is easily solved by trying all possible numbers of large packages and calculating the number of small packages needed to achieve ~G~ units. The solution is the smallest cost over all choices for the number of large packages.

Now we can check if we have enough ingredients for ~S~ servings of the meal. For each ingredient, we know how many units we need for ~S~ servings and we can calculate the cost for that many servings using the above algorithm. If we have enough money to buy all needed ingredients, then we can prepare ~S~ servings.

A solution that increments ~S~ while we can prepare ~S~ servings will score ~90\%~ of points. To obtain the full score, use binary search to find the largest ~S~ such that we can prepare ~S~ servings.