$19.$ Techsburg, Inc. uses a stamping machine to manufacture aluminum bodies for lightweight miniature aircraft used for military reconnaissance. Currently, forms in the stamping machine are changed after every $60$ hours of operation or whenever a form breaks, whichever happens first. The lifetime of each form follows a Weibull distribution with location, scale, and shape parameters of $50,25,$ and $2,$ respectively. The machine is operated $5840$ hours per year. It costs $$800$ to replace the stamping forms. If a form breaks before its scheduled replacement time $($or in less than $60$ hours of use$),$ the shop loses $8$ hours of production time. However, if a form lasts until its scheduled replacement after $60$ hours of use, the shop only loses $2$ hours of production time. The company estimates that each hour of lost production time costs $$1200.*$On average, how much does Techsburg spend maintaining this stamping machine per year? $*$Suppose Techsburg wanted to minimize its total maintenance cost for the stamping machine. How often should the company plan on changing the stamping forms and how much money would it save? $*$ Suppose the cost to replace the stamping forms is expected to increase. What impact should this have on the optimal planned replacement time of the forms?Explain. $*$ Suppose the cost of lost production time is increased. What effect should this have on the optimal planned replacement time of the forms? Explain.