b$)$ A retailer the with make$-$to$-$order setting for high$-$end bed frames wants to decide what menu of products to offer to maximize its expected profit. The retail can offer the following four different sizes of bed frames: Twin, Full, Queen, and King. The customer preference and profit margin of each size is given below. The store traffic is $100$ and the fixed variety cost is $10.$ Please consider the no$-$purchase choice v$0=6.$