Question $1)$ In the class we studied a greedy algorithm for the knapsack problem with the

following objects:

The total capacity of the knapsack is $M=15$ pounds. For this problem, we defined this objective:

Price

$\frac{\text{P}\text{r}\text{i}\text{c}\text{e}}{\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}}$ to choose the best item with the highest price and lowest weight in each step.

a$)$ Now, let's define another greedy method where the objective is only Price $($we choose

items with the highest Price instead of $\frac{\text{P}\text{r}\text{i}\text{c}\text{e}}{\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}}$ in each step$).$

What is the total profit and total weight of this solution compared to the solution in our

class?

b$)$ Let's change the objective to weight $($we choose items with the lowest weight instead of

the highest $\frac{\text{P}\text{r}\text{i}\text{c}\text{e}}{\text{W}\text{e}\text{i}\text{g}\text{h}\text{t}}).$

What is the total profit and total weight of this solution compared to the solution in our

class?