Question

A company makes electronic gadgets. 2% are faulty, the company doesn't know which ones are faulty until a buyer complains. Suppose the company makes a $147 profit on each sale, but has to refund the sale price and suffers a loss of $10 for every faulty gadget because they have to repair the unit. What is the profit(or loss) the company can expect to make from selling 100 units?.

Answer 1

To calculate the expected profit (or loss) from selling 100 units with 2% of them being faulty, we can follow these steps:

1. Determine the number of faulty units:

   • 2% of 100 units = 0.02 * 100 = 2 units.

2. Calculate the profit from non-faulty units:

   • If there are 98 non-faulty units, the profit from these is: \[ \text{Profit from non-faulty units} = 98 \text{ units} \times 147 \text{ dollars/unit} = 14,406 \text{ dollars}. \]

3. Calculate the loss from faulty units:

   • The company has to refund the price for each faulty unit (which is what the customer pays for it, essentially the same as the profit minus the loss). For each faulty unit:
     • The loss incurred for each faulty unit after repairing and refunding will be: \[ \text{Loss per faulty unit} = 147 \text{ dollars} - 10 \text{ dollars} = 137 \text{ dollars} \]
     • Therefore, for 2 faulty units: \[ \text{Total loss from faulty units} = 2 \text{ units} \times (147 + 10) \text{ dollars/unit} = 2 \times 157 = 314 \text{ dollars}. \]

4. Calculate the total expected profit/loss:

   • The total profit from selling 100 units minus the total loss from faulty units will be: \[ \text{Total profit} = \text{Profit from non-faulty units} - \text{Total loss from faulty units} \]

   • Plugging in the numbers: \[ \text{Total profit} = 14,406 \text{ dollars} - 314 \text{ dollars} = 14,092 \text{ dollars}. \]

Thus, the expected profit from selling 100 units is $14,092.