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:

Item Profit per Unit Steel $($lb$.)$ Fabric $($lb$.)$ Labor $($Hr$.)$

Chain mail $453524$

Plate armor $758348$

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