A baseball bat workshop makes two models of bats, the "slugger" and the inhacker. Each slugger requires four minules of lathe work, and one minute vamishing. Each whacker requires five minutes of lathe work and $45$ seconds vamishing.

Each day, the combined production cannot exceed $980$ bats. The woodworking shop operales $16$ hours$/$day$,$ with one room containing five lathes, and one vamishing room. Each of the five lathes is available for $55$ minutes each hour, and the vamishing room is available for $50$ minules each hour.

Each slugger contribules $5$ to profil, and each whacker contributes $6.$

The workshop wishes lo delermine how many sluggers and whackers should be made each day.

a$)$ Formulale a Linear Programming model to maximize profits for this problem. Cleaty define and label the decision variables, the objective function ano the constrainls.

$(10$ marks$)$ Gollowing sen Excel Solver.