f$.$ Solve this problem using linear programming.

$7.$ A scene is being shot for a film. A total of $11$ distinct activities have been identified for the filming. First, the script must be verified for continuity, the set erected and decorated, and the makeup applied to the actors. After the set is completed, the lighting is set in place. After the makeup is applied, the actors get into costume. When these five activities are completed, the first rehearsal of the scene commences, which is followed by the second scene rehearsal with the cameraperson. While the rehearsals are going on$,$ verifications of the audio and the video equipment are made. After both rehearsals and verifications are completed, the scene is shot. Afterward, it is viewed by the director to determine if it needs to be reshot.

Listed below are the activities and the time required for each activity.

$\backslash$table$[[$Activity$,\backslash$table$[[$Time Required$],[($days$)]]],[$A$.$ Check script for story continuity,$2\mathrm{.}0],[$B$.$ Decorate set; place necessary props,$4\mathrm{.}5],[$C$.$ Check lighting of scene,$1\mathrm{.}0],[$D$.$ Apply makeup to actors,$0\mathrm{.}5],[$E$.$ Costumes for actors,$1\mathrm{.}5],[$F$.$ First rehearsal $($actors only$),2\mathrm{.}5],[$G$.$ Video verification,$2\mathrm{.}0],[$H$.$ Sound verification,$2\mathrm{.}0],[$I$.$ Second rehearsal $($with camera and lights$),2\mathrm{.}0],[$J$.$ Shoot scene,$3\mathrm{.}5],[$K$.$ Director's OK of scene,$1\mathrm{.}5]]$