$($All answers were generated using $1,000$ trials and native Excel functionality.$)100,$ Galaxy sells only the $100$ pairs of goggles in stock. Galaxy assigns a shortage cost of $$40$ for each unit of demand that is unsatisfied to represent a loss$-$of$-$goodwill among its customers. Management would like to use a simulation model to analyze this situation.

$($a$)$ What is the average monthly profit resulting from its policy of stocking $100$ pairs of goggles at the beginning of each month? Round your answer to the nearest dollar.

$($b$)$ What is the proportion of months in which demand is completely satisfied? Round your answer to the nearest whole number.

$\%$ The average difference between the net profit generated by a replenishment level of $120$ versus a replenishment level of $100$ is $$,$ It means that monthly replenishment level of $-$ Select your answer $-1$ increases profitability.