Salvatore Genovesi $($SG$)$ is a high$-$end luxury fashion brand. The SG women's cotton blend shirts, sold in the fall season, are priced at p$=$$$400.$ The production cost is c$=$$$180.$ The product's ability to meet consumers' needs is uncertain, leading to two potential post$-$purchase outcomes: a "good match" or a "bad match." The likelihood of it being a good match is represented by g$=0\mathrm{.}9($with a bad match being $1-$g$).$ Considering the potential risk of ending up with a product that may not be the right fit, consumers might hesitate to make a purchase initially. In an effort to mitigate this risk, the company provides a return option to consumers. Consequently, after acquiring and assessing the product, consumers decide whether to retain and use the product $($if it's a good match$)$ or return the product $($if it's a bad match$)$ to the company for a refund. If consumers decide to return their unwanted product, they gain a refund r$=$$$300$ from SG$.$ The returned products and leftover products during the fall season are discounted to b$=$$$140$ in a special sales season just before the start of the winter season. Let's designate the inventory level as q$.$ Demand is uncertain, and the distribution is known. Assume that demand for the product distribution is fairly closely approximated by a normal distribution with mean $20$ and standard deviation $6.$ How many products should SG produce