Answer:
To solve this fractional knapsack problem using the criteria of maximizing profit per unit capacity at each step, we need to calculate the profit per unit capacity for each object.
For object 1, profit per unit capacity = p1/w1 = 13/1 = 13. For object 2, profit per unit capacity = p2/w2 = 20/2 = 10. For object 3, profit per unit capacity = p3/w3 = 14/4 = 3.5. For object 4, profit per unit capacity = p4/w4 = 15/3 = 5.
We can see that object 1 has the highest profit per unit capacity, so we should choose it first.
After choosing object 1, the weight capacity remaining in the knapsack is 5-1=4.
Next, we need to calculate the profit per unit capacity for the remaining objects: For object 2, profit per unit capacity = p2/w2 = 20/2 = 10. For object 3, profit per unit capacity = p3/w3 = 14/4 = 3.5. For object 4, profit per unit capacity = p4/w4 = 15/3 = 5.
We can see that object 2 has the highest profit per unit capacity among the remaining objects, so we should choose it next.
After choosing object 2, the weight capacity remaining in the knapsack is 4-2=2.
Next, we need to calculate the profit per unit capacity for the remaining objects: For object 3, profit per unit capacity = p3/w3 = 14/4 = 3.5. For object 4, profit per unit capacity = p4/w4 = 15/3 = 5.
We can see that object 4 has the highest profit per unit capacity among the remaining objects, so we should choose it next.
After choosing object 4, the weight capacity remaining in the knapsack is 2-3=-1, which means that we cannot choose any more objects as we have run out of weight capacity in the knapsack.
Therefore, the optimal solution is to choose objects 1, 2, and 4 in that order, for a total profit of 13+20+15=48.
Step-by-step explanation: