A Plant Manager for a Sporting Goods Manufacturer Is in Charge

A plant manager for a sporting goods manufacturer is in charge of assigning the manufacture of four new aluminum products to four different departments.Because of varying expertise and workloads,the different departments can produce the new products at various rates.If only one product is to be produced by each department and the daily output rates are given in the table below,which department should manufacture which product to maximize total daily product output? (Note: Department 1 does not have the facilities to produce golf clubs.) $$\begin{array} { c c c c c } \hline \text { Department } & \begin{array} { c } \text { Baseball } \\\text { Bats }\end{array} & \begin{array} { c } \text { Tennis } \\\text { Rackets }\end{array} & \begin{array} { c } \text { Golf } \\\text { Clubs }\end{array} & \begin{array} { c } \text { Racquetball } \\\text { Rackets }\end{array} \\\hline 1 & 100 & 60 & X & 80 \\2 & 100 & 80 & 140 & 100 \\3 & 110 & 75 & 150 & 120 \\4 & 85 & 50 & 100 & 75 \\\hline \hline\end{array}$$ Formulate this assignment problem as a linear program.