To calculate the expected profit (or loss) from producing 100 units, we need to find out how many of these units are expected to be faulty, the profit from the non-faulty units, and the loss from scrapping the faulty units.
Step 1: Determine the number of faulty units.
The percentage of faulty gadgets is 3.5%. So, for 100 units:
\[ \text{Number of faulty units} = 100 \times 0.035 = 3.5 \]
Since we can't have a fraction of a unit in practical terms, we can expect either 3 or 4 faulty units. For expected profit calculations, we will use the average, which we'll round as appropriate later.
Step 2: Calculate the number of non-faulty units.
The number of non-faulty units is:
\[ \text{Number of non-faulty units} = 100 - \text{Number of faulty units} \]
If we use the average expected number of faulty units (3.5), then:
\[ \text{Number of non-faulty units} = 100 - 3.5 = 96.5 \]
Step 3: Calculate profit from non-faulty gadgets.
The profit per non-faulty gadget is $201. Therefore, the profit from the non-faulty gadgets is:
\[ \text{Profit from non-faulty units} = 96.5 \times 201 = 19351.5 \]
Step 4: Calculate loss from faulty gadgets.
The loss per faulty gadget is $11. The total loss from the expected number of faulty gadgets is:
\[ \text{Loss from faulty units} = 3.5 \times 11 = 38.5 \]
Step 5: Calculate total expected profit (or loss).
The total expected profit (considering the loss from faulty units) is:
\[ \text{Total expected profit} = \text{Profit from non-faulty units} - \text{Loss from faulty units} \] \[ \text{Total expected profit} = 19351.5 - 38.5 = 19313 \]
Conclusion
The expected profit the company can expect to make from producing 100 units is $19,313.