Nonlinear Optimization in Feasible Region Conceptual Overview: Explore how the optimal point is chosen from the feasible set when the optimization function is nonlinear. Par, Inc. manufactures both standard and deluxe golf bags. A prior applet established the feasible region in the graph below. The highlighted region represents feasible combinations of the number of standard and deluxe golf bags that could be manufactured given Par, Inc.'s production constraints. The profit contribution from each type of bag is quadratic and their sum represents the total profit; that is, 80 S - (1/15)52 + 15 D-(1/5)02. The maximum possible profit is $52,125 when S = 600 and D = 375, represented by a red point in the graph. However, this point is outside the feasible region so is not a possible production value. The profit equation defines the ellipse shown in the graph, along with the value of the profit function for the ellipse. The optimal feasible point is when an ellipse just touches the feasible region. Drag on the graph to expand and contract the ellipse until it just touches the feasible region. About what are the number of S and D bags represented by that point? Due to the resolution of the screen, it is difficult to place the ellipse exactly on the best single point in the feasible region. Once you are close, double click on the graph and the ellipse will move to the optimal position. 700 600- 500 $51,000.00 400 Number of Deluxe Bags 200 100 0 0 100 200 300 400 500 600 700 800 Number of Standard Bags 1. What is the approximate maximum possible profit achieved without violating constraints? a. 45,894 b. 48,918 C. 49,921 d. 52,125 b 2. What is the approximate number of Standard Bags to produce to achieve the maximum possible profit without violating constraints? a. 308 b. 375 C. 459 d. 600 3. What is the approximate number of Deluxe Bags to produce to achieve the maximum possible profit without violating constraints? a. 308 b. 375 C. 459 d. 600 b Nonlinear Optimization in Feasible Region Conceptual Overview: Explore how the optimal point is chosen from the feasible set when the optimization function is nonlinear. Par, Inc. manufactures both standard and deluxe golf bags. A prior applet established the feasible region in the graph below. The highlighted region represents feasible combinations of the number of standard and deluxe golf bags that could be manufactured given Par, Inc.'s production constraints. The profit contribution from each type of bag is quadratic and their sum represents the total profit; that is, 80 S - (1/15)52 + 15 D-(1/5)02. The maximum possible profit is $52,125 when S = 600 and D = 375, represented by a red point in the graph. However, this point is outside the feasible region so is not a possible production value. The profit equation defines the ellipse shown in the graph, along with the value of the profit function for the ellipse. The optimal feasible point is when an ellipse just touches the feasible region. Drag on the graph to expand and contract the ellipse until it just touches the feasible region. About what are the number of S and D bags represented by that point? Due to the resolution of the screen, it is difficult to place the ellipse exactly on the best single point in the feasible region. Once you are close, double click on the graph and the ellipse will move to the optimal position. 700 600- 500 $51,000.00 400 Number of Deluxe Bags 200 100 0 0 100 200 300 400 500 600 700 800 Number of Standard Bags 1. What is the approximate maximum possible profit achieved without violating constraints? a. 45,894 b. 48,918 C. 49,921 d. 52,125 b 2. What is the approximate number of Standard Bags to produce to achieve the maximum possible profit without violating constraints? a. 308 b. 375 C. 459 d. 600 3. What is the approximate number of Deluxe Bags to produce to achieve the maximum possible profit without violating constraints? a. 308 b. 375 C. 459 d. 600 b
