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Thinking if it is a Knapsack problem.

Here is the scenario:

Michael and his daughter (7 year old kid) enjoy going to cinema for movies.

Weekdays fare for kids is 5 dollars, adult 8.
Weekend fare $12.00, regardless kid or adult.

With $100 budget, how can Michael and his daughter enjoy more movies, considering most of those falls in weekdays?

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So it costs \$13 for the two of them on a weekday and \$24 for the two of them on a weekend. If you want to maximize the number of movies, skip the expensive ones and the \$100 budget yields $\lfloor 100/13 \rfloor = 7$ movies.

If you prefer writing it explicitly as an optimization (yes, knapsack) problem, let integer decision variables $x$ and $y$ be the numbers of weekday and weekend movies attended, respectively. The problem is to maximize $x+y$ subject to linear constraints \begin{align} 13x+24y &\le 100 \\ x &\ge 0 \\ y &\ge 0 \end{align} The unique optimal solution is $(x,y)=(7,0)$, with objective value $7+0=7$.

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    $\begingroup$ thank you for the guidance! that's fantastic! $\endgroup$
    – Mark K
    Dec 31 '20 at 6:22

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