(I'm trying to figure out how to word it. This is my first time taking a math class in a long time. Any assistance would be appreciated. Thanks.)

A company makes wooden tables in two varieties. One is a round kitchen table. The second is one with two leaves, which makes it appropriate for dining rooms. Sales of both of these tables have been excellent. In fact, there is more demand for both of them than can be met with the existing manufacturing capacity. There is a higher profit margin on the table with the leaves, but this table requires more time on the planer machine, which has been used to its capacity. It is desired to whether the higher profit margin is enough to justify the current manufacturing strategy of making the table with the leaves exclusively. The profit margins are $43 round table and $49 table with leaves. The manufacturing operations require time on the lathe to make legs, time on the planer to make the top and leaves and some hand-finishing time.

Machine (Time in minutes)

Table Lathe Planer Hand-finishing

Round 9 7.8 15

Leaves 9 10.8 18

The shop works seven days a week and 24 hours a day. There are two people who work each shift to do the hand-finishing. One person per shift to work the other two jobs. Formulate the linear programming model to determine the best product mix. Graphically represent the model, labeling all lines, points, isoprofit line, identify the feasible area, and solve.

What kind of constraint is the hand-finishing constant? Why do you need it? Make a change in the model to demonstrate sensitivity analysis and resolve.