To determine the marginal product of the 40th input item, let's first understand what the marginal product is. The marginal product (MP) is defined as the additional output produced when one more unit of input is added.
To find the marginal product of the 40th input item, we need to consider the change in the total product when the input increases from 30 to 40 units.
Here are the steps for calculating the marginal product:
1. Identify the previous and current levels of input and output:
- Previous input level: 30
- Output at this previous input level: 720
- Current input level: 40
- Output at this current input level: 820
2. Calculate the change in output:
[tex]\[
\Delta \text{Output} = \text{Output at current input level} - \text{Output at previous input level} = 820 - 720 = 100
\][/tex]
3. Calculate the change in input:
[tex]\[
\Delta \text{Input} = \text{Current input level} - \text{Previous input level} = 40 - 30 = 10
\][/tex]
4. Compute the marginal product (MP):
[tex]\[
\text{Marginal Product} = \frac{\Delta \text{Output}}{\Delta \text{Input}} = \frac{100}{10} = 10.0
\][/tex]
Therefore, the marginal product of the 40th input item is 10.0. This matches none of the given multiple choices (80 and 20.5), indicating that there might have been an error in the provided options. The correct marginal product is 10.0.
