CleanAir, a new lightweight air purifier, has been test$-$marketed at several large box stores in the Denver area.$$ After a successful test market, the developers have decided to launch the product nation$-$wide so they are looking for venture capitalists to invest. Here is the sales data that they have provided for you to consider:$$

Based on the test market, sales predictions for the CleanAir are as follows:$$

Units Sold

Probability

$2500$

$0\mathrm{.}15$

$5000$

$0\mathrm{.}45$

$7500$

$0\mathrm{.}40$

$$Fixed costs for the production is Normally Distributed with a mean of$$$$180,000$and a standard deviation of$$$$25,000.$

Variable cost is$$$$20$per unit and the selling price is$$$$79.$

a$)$ In Excel, use simulation to calculate the expected net profit. Run $25$ trials simulating the demand and the costs. Find the average net profit for the $25$ trials.$$