You are an owner of a firm that manages other small manufacturing companies, which pay you to employ temporary salespersons to sell their products. The owner of one of these firms wants to increase their sales and promised to give you a bonus of $12,000 if your temp salespeople sell at least 10 products tomorrow. Assume the cost of a single sales visit a temp sales reps cost you $100 and only a single visit per sales rep per day is allowed. Give that the probability of making a single sale is 0.20, determine the number of temporary salespersons you should plan to hire in order to maximize your profit.
To determine the number of temporary salespersons you should hire to maximize your profit, we need to analyze the cost and potential revenue for each scenario.
Let's consider the different possibilities:
1. Hiring zero salespersons:
- Cost: $0
- Probability of selling at least 10 products: 0% (since there are no salespersons)
- Expected revenue: $0
- Bonus: $0
- Profit: $0
2. Hiring one salesperson:
- Cost: $100
- Probability of selling at least 10 products: 0.20 (as given)
- Expected revenue: 0.20 x 10 x $100 = $200
- Bonus: $0 (since the sales target is not met)
- Profit: $200 - $100 = $100
3. Hiring two salespersons:
- Cost: $200
- Probability of selling at least 10 products: 0.20 (as given)
- Expected revenue: 0.20 x 10 x 2 x $100 = $400
- Bonus: $0 (since the sales target is not met)
- Profit: $400 - $200 = $200
4. Hiring three salespersons:
- Cost: $300
- Probability of selling at least 10 products: 0.20 (as given)
- Expected revenue: 0.20 x 10 x 3 x $100 = $600
- Bonus: $0 (since the sales target is not met)
- Profit: $600 - $300 = $300
Now, if we analyze the scenarios, we can observe that hiring more than one salesperson will not give us the desired profit since the bonus of $12,000 is much higher than the additional revenue. Therefore, we should hire only one salesperson.
To maximize profit, hire only one temporary salesperson.