The Notip Table Company sells two models of its patented five-leg tables. The basic version uses a wood top, requires 0.6 hour to assemble, and sells for a profit of $200. The deluxe model takes 1.5 hours to assemble because of its glass top, and sells for a profit of $350. Over the next week the company has 300 legs, 50 wood tops, 35 glass tops, and 63 hours of assembly available. Notip wishes to determine a maximum profit production plan assuming that everything produced can be sold.

(a) Formulate a mathematical programming model with 4 main constraints to select an optimal production plan using decision variables x1 ! number of basic models produced and x2 ! number of deluxe models.

(b) Enter and solve your model with the class optimization software.

(c) Using a 2-dimensional plot, solve your model graphically for an optimal product mix, and explain why it is unique.

(d) On a separate 2-dimensional plot, show that the model has alternative optimal solutions if profits are $120 and $300, respectively.