The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on hand inventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).

The correct answer is 110.

1. Understanding the Product Structure Diagram (Bill of Materials)
Based on the provided product structure tree shown in the image, we can trace the requirements for producing 1 unit of the final product P (at Level 0):
• Level 1: Under product P, we require 4 units of component A and 2 units of component B. This is represented as A(4) and B(2).
• Level 2: Under component B, we require 1 unit of component C and 3 units of component D. This is represented as C(1) and D(3).
• Level 3: Under component D, we require 2 units of component A. This is represented as A(2).

2. Step-by-Step Calculation for 10 Units of Product P

Step 2a: Direct requirement of component A at Level 1
Each unit of P requires 4 units of A. Therefore, for 10 units of P:
$$\text{Direct A Required}=10\times 4=40\text{ units}$$

Step 2b: Requirement of component B at Level 1
Each unit of P requires 2 units of B. Therefore, for 10 units of P:
$$\text{B Required}=10\times 2=20\text{ units}$$

Step 2c: Requirement of component D at Level 2
Each unit of B requires 3 units of D. Therefore, to manufacture the 20 units of B calculated above:
$$\text{D Required}=20\times 3=60\text{ units}$$

Step 2d: Indirect requirement of component A at Level 3
Each unit of D requires 2 units of A. Therefore, to manufacture the 60 units of D calculated above:
$$\text{Indirect A Required}=60\times 2=120\text{ units}$$

3. Total Requirement of Component A
Summing both the direct and indirect requirements for component A:
$$\text{Total A Required}=40+120=160\text{ units}$$

4. Additional Component A Needed
We are given that there is already an on-hand inventory of 50 units of component A. The number of additional units needed is:
$$\text{Additional A Needed}=\text{Total Required}-\text{On-Hand Inventory}$$
$$\text{Additional A Needed}=160-50=110\text{ units}$$

Thus, the additional number of units of component A required is 110.