$1.(50$ points$)$ In class lecture, we developed a simple spreadsheet model for computing profit in Excel. Use this profit model to implement a financial simulation model for a new product proposal and determine a distribution of profits using the distribution below for the demand, unit cost, and fixed cost. Price is fixed at $$1,000.$ Demand is unknown and follows a normal distribution with a mean of $150$ and a standard deviation of $20.$ Fixed costs are uniformly distributed between $$45,000$ and $$55,000.$ Unit costs are also variable and follow the following distribution:

Unit Cost

Probability

$$400$

$0\mathrm{.}20$

$$600$

$0\mathrm{.}40$

$$700$

$0\mathrm{.}25$

$$800$

$0\mathrm{.}15$

$$

Simulate this model for $50$ trials and a production quantity of $200.$ What is the average profit and what is the standard deviation of profit?