A firm considers producing three different dining tables: X1, X2, and X3. Machine hours to produce each dining table, unit profits, and the available machine hours are as the following:

The marketing department forecasts that they can sell all the X1 and X2 that will be produced. Yet, the sales potential of X3 is at most 80 units per period. The optimal product mix and the corresponding answer/sensitivity reports obtained from Excel Solver are provided below:

i. What is the idle time for each machine under the optimal production plan?

ii. Suppose an additional 200 hours per week can be obtained from the milling machines by using staff overtime for an additional $1.50 of overtime cost per hour. Would you recommend doing this and what is the effect of doing that on the total profit?

Milling machine Lathe Grinder Unit profit X1 8 4 2 $20 Machine Product hours X2 X3 2 3 800 3 0 480 0 11 320 $6 $8 Answer Report Objective Cell (Max) Cell Name $C$9 Profit Value Original Value $0 Final Value $2,140 Original Value Variable Cells Cell Name $C$3 X1 # of Production $C$4 X2 # of Production $C$5 X3 # of Production uction Original value Final Value Final Value 45 100 80 Integer Contin Contin Contin Slack Constraints Cell Name $C$13 Milling LHS $C$14 Lathes LHS $C$15 Grinders LHS $C$16 X3 LHS $C$17 X1 LHS $C$18 X2 LHS $C$19 X3 LHS Cell Value 800 480 170 80 45 100 80 Formula $C$13=$D$17 $C$18>=$D$18 $C$19>=$D$19 Status Binding Binding Not Binding Binding Not Binding Not Binding Not Binding 150 0 45 100 80 Sensitivity Report Variable Cells Allowable Decrease Cell $C$3 $C$4 $C$5 Name X1 # of Production X2 # of Production X3 # of Production Final Reduced Value Cost 45 0 100 0 Objective Allowable Coefficient Increase 20 2.222222222 6 1.25 Constraints 200 Cell Name $C$13 Milling LHS $C$14 Lathes LHS $C$15 Grinders LHS $C$16 X3 LHS $C$17 X1 LHS $C$18 X2 LHS $C$19 X3 LHS Final Shadow Constraint Value Price R.H. Side 800 2.25 800 480 0.5 480 320 1.25 80 45 0 0 1000 0 800 0 170 80 Allowable Allowable Increase Decrease 400 240 360 200 1E+30 150 80 80 45 1E+30 1E+30 801E+30