Problem $4$: $(25$ points$)$ A factory is manufacturing TVs$.$ The amount of TV manufactured each week is normally distributed with mean $200,$ and standard deviation $20.$ Each week, the factory receives an order from a private retail partner in Australia. The orders from the private retail partner in Australia can only be $10,20,30$ or $40,$ which follows the following empirical distribution:

Incubation Machine Time $($min$)$

$10$

$20$

$30$

$40$

Percent of Samples

$15\%$

$23\%$

$27\%$

$35\%$

The remaining inventory $($i$.$e$.,$ the difference between the manufactured amount and the order quantity from the Australian retail partner$)$ can be sold to retailers in Europe. For planning purposes, the operations manager would like to estimate the amount that the factory could sell to European retailers each week.

Please create a spreadsheet model to simulate the amount of the TVs that the factory could sell to European retailers for the first $100$ weeks. Please include your Excel simulation model in your homework submission. What's the mean and standard deviation of the amount of the TVs that could be sold to European retailers each week? PLEASE SHOW EXCEL AND SHOW EXCEL AND FORMULAS