Solution to Knapsack Problem

Given parameters:
n = 3 (number of items)
M = 15 (maximum weight capacity of the knapsack)
P1 P2 P3 = (25,24,15) (profit of each item)
W1 W2 W3 = (18,15,10) (weight of each item)

Step 1: Calculate the profit-to-weight ratio for each item
- Profit-to-weight ratio for item 1 = P1/W1 = 25/18 = 1.3889
- Profit-to-weight ratio for item 2 = P2/W2 = 24/15 = 1.6
- Profit-to-weight ratio for item 3 = P3/W3 = 15/10 = 1.5

Step 2: Sort the items in decreasing order of their profit-to-weight ratios
- Item 2 has the highest profit-to-weight ratio, followed by item 1 and then item 3

Step 3: Add items to the knapsack in order of their profit-to-weight ratios until the knapsack is full or all items have been added
- Add item 2 to the knapsack (weight = 15, profit = 24)
- Add item 1 to the knapsack (weight = 18+15 = 33 > M, cannot be added)
- Add item 3 to the knapsack (weight = 15+10 = 25 > M, cannot be added)

Step 4: Calculate the total profit of the items in the knapsack
- Total profit = 24 + 15 = 39

Step 5: Output the optimal solution
- The optimal solution is to select items 2 and 3 for a total profit of 39 and a total weight of 25, which is within the weight capacity of the knapsack.

Answer is - price 24 units
price/weight ratio is max for product 2
weight of product 2 =15, which is also the max weight allowed