Wiglaf is a small$-$time, profit$-$maximizing blacksmith that produces armor for his local lord. His team only produces chain mail and plate armor. Both items require steel, fabric and labor. He's collected the following data on these products:

$\backslash$table$[[$Item$,$Profit per Unit,Steel $($lb$.),$Fabric $($lb$.),$Labor $($Hr$.)],[$Chain mail,$45,3,5,24],[$Plate armor,$75,8,3,48]]$

Wiglaf determines that he only has $60lb.$ of steel, $48lb.$ of fabric and $320hr.$ of labor.

a$)$ Formulate this as an LP written math problem: state the decision variables, objective function, and list all the constraints. No need to solve it yet or make an Excel model.

b$)$ Now Wiglaf discovers that due to lackluster manufacturing, half of the total available fabric is unsuitable to be used in chain mail. Further Wiglaf learned there is a new law that at least $50\%$ of labor hours used must go towards plate armor. Create an Excel LP model including this new constraint. Solve the model using Excel Solver. Provide an image of your model, solver screen, and report the optimum solution. Round decimals to the nearest hundredth.