An online company sells handmade samurai katana swords. the website costs $ 475 a month to maintain. each katana costs $ 200 to make, and they sell each katana for $ 755. create a linear model in the form y = m x + b where x is the number of swords sold per month and y is the net monthly profit. using this model, find the number of swords that would need to be sold per month to have a monthly profit of $ 4370.,

For each sword sold, the revenue is $755 and the variable cost is $200; thus the contribution per unit is $755-200 = $555. The monthly fixed cost, which counts against aggregate profit, is $475. Thus the total profit y as a function of swords sold x can be written as y = $555x - $475. As such, in order to yield a profit of 4370, 555x must equal 4370+475 = 4845. Dividing by 555 and rounding up, we find that 9 swords would need to be sold per month.