The Y Company sells two models of its patented technology. The basic version uses 100 square-feet of aluminum, requires 0.6 hours to assemble, and sells for a profit of $200. The deluxe model uses 100 square-feet of platinum, takes 1.5 hours to assemble, and sells for a profit of $350. Both versions require 5 hours of detail work. Over the next week the company has 5,000 square-feet of aluminum, 3,500 square-feet of platinum, 300 hours of detail expertise available, and 63 hours of assembly labor available. The Y Company wishes to determine a maximum profit production plan assuming that everything produced can be sold. Use A linear program model for selecting an optimal production plan using decision variables: x1 = the number of basic models produced next week x2 = the number of deluxe models produced next week
**Linear Model Established already::::**
z=200×1+350×2
subject to: x1
x2
5×1+5×2
.6×1+1.5×2
a. Find the intersection points of the inequalities in the positive x1 and x2 quadrant where the inequalities define the LP’s feasible region.
b. Using a two-dimensional plot, solve your model graphically for an optimal product mix. To receive full credit, your feasible region must be graphed correctly, and the optimal solution, which includes the decision variable values and the objective function value at optimality, need to be provided.
c. On a separate two-dimensional plot, show that the model has alternative optimal solutions if profits are $120 and $300 for the basic and deluxe models, respectively. Briefly describe what this means from a graphical perspective.
