1. Virtual Reality Goggle Inventory. Galaxy Co. sells virtual reality (VR) goggles, particularly targeting customers who like to play video games. Galaxy procures each pair of goggles for $150 from its supplier and sells each pair of goggles for $300. Monthly demand for the VR goggles is a normal random variahle with a mean of 160 units and a standard deviation of 40 units. At the beginning of each month, Galaxy orders enough goggles from its supplier to bring the inventory level up to 140 goggles. If the monthly demand is less than 140, Galaxy pays $20 per pair of goggles that remains in inventory at the end of the month. If the monthly demand exceeds 140, Galaxy sells only the 140 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. Whatis the average monthly profit resulting from its policy of stocking 140 pairs of goggles at the beginning of each month? b. What is the proportion of months in which demand is completely satisfied? c. Use the simulation model to compare the profitability of monthly replenishment levels of 140 and 160 pairs of goggles. Use a 95% confidence interval on the difference between the average profit that each replenishment level generates to make your comparison