2-1 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 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) O Formulate a mathematical programming model with 4 main constraints to select an op- timal production plan using decision variables x A number of basic models produced and x2 A number of deluxe models. (b) O QEnter and solve your model with the class optimization software. (c) Using a two-dimensional plot, solve your model graphically for an optimal product mix, and ex- plain why it is unique. (d) O On a separate two-dimensional plot, show that that the model has alternative optimal so- lutions if profits are $120 and $300, respectively.