$7.(15$ points$)$ A $2019$ master schedule for table assembly for the AJE furniture company is as follows, where each entry represents the weekly production during the stated month:

To assemble a table, four legs must be lathed, the tabletop must be planed, and four holes must be drilled to accommodate the legs. The total time required in each of these three work centers to complete the components for one table are:

There are six lathes, three planes, and one and half drills $($the second drill is shared with another product line$),$ each available for two shifts per day, five days per week, eight working hours per shift. Overtime is available for a maximum of two hours per day per machine and for eight hours per machine on the weekend. Historical utilization of all three work centers is $\backslash (95\backslash \%\backslash ).$ The rated efficiency of the lather, plane, and drill work centers is $\backslash (105\backslash \%,112\backslash \%\backslash ),$ and $\backslash (102\backslash \%\backslash ),$ respectively. Prepare a machine load report for each work center for the year and indicate whether adequate capacity exists to meet the master production schedule. If there is not sufficient capacity to meet the schedule, make recommendations about what the AJE furniture company could do$.$