I CAT $28$ NOVEMBER $20232-4$PM ATTEMPT ALL QUESTIONS A$.$ Air Kenya operates airplanes out of JKIA. Due to its schedule for flights, differing number of ground personnel are required throughout the day. The table below shows how many ground personnel are required to be on duty during each four$-$hour period in the day. For example, from $4$pm to $8$pm$,$ the airline needs $47$ ground personnel on duty. In the situation outlined Air Kenya wishes to assign personnel, who work eight consecutive hours, in a manner which will minimize the total number of ground personnel employed. Set up a linear programming model $(12$ marks$)$ that for Air Kenya $($DO NOT SOLVE THE MODEL$).$ Time of day $12$am$-4$am Personnel required $104$am$-8$am $248$ am$-12$pm $3912$pm$-4$ pm $434$pm$-8$pm $47288$pm$-12$am B$.$ XYZ company manufactures two products Regular $($X$)$ and Deluxe $($Y$)$ The LP model used to determine the production schedule is as follows: Maximize profit $(2)=35$x$+68$Y Subject to: $7$x$+10$y $=<3000($labour hours$)3$x $+2$y $=<900($total units demanded$)4$x $+5$y $=<2000($raw materials$)$ all variables $0$ Using the simplex method determine $1.$ iv The final tableau How many units of X should the company produce? How many units of Y $3$ Marks should the company produce? $3$ marks What is the optimal profit? $2$ marks $10$ marks How may units of labour will be used to give the optimal profit? $2$ marks Question Two certain project being implemented by the Kenyan government, the project manager identified and documented vi$.$ Which resource is most constraining? $2$ marks vii. Assuming the company can only access $1000$ labor hours determine the number of X and Y units to be produced, optimal profit and amount of raw materials used. $10$ marks In a the following details: Activity Predecessor $$ Optimistic Lime Most likely time Pessimistic Time Normal Crash time $($expected$)$ Cast $($KShs$)$ Crash cost$($KShs$)12181400618004180042400612181800121800$ A$,$ B $1222001023001$