The name "knapsack problem" dates back to the early works of mathematician$$Tobias Dantzig$(18841956),$and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. The question is: which boxes should be chosen to maximize the amount of money while keeping the overall weight under or equal to $15$ kg$?$ Assume that only one of each box is available and you can only either take the whole of a box or nothing at all.

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a$.$ Solve the Knapsack problem in Solver and tell me your strategy below. Which boxes would you take? $(1$ point$)$

$($You can name the boxes using their colors: green, gray, orange, yellow, and blue.$)$

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b$.$ What happens to your solution when you want to include the yellow box but don't want to include the blue box? $(1$ point$)$

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c$.$ What happens to your solution $($in part $($a$))$ when you want to include at least one of the green or the orange boxes? $(1$ point$)$

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$($Please solve different parts in different tabs$.)$