Time Hoursproduct Assembly Packagingmodel A15m Time Hoursproduct Assembly Packagingmodel A15m TIME (hours) PRODUCT Assembly Packaging Model A 1 .5 Model B 1.5 .33 Write two constraints, one that represents the limits of only 800 hours in Assembly and one that represents only 100 hours available in Packaging. Let A represent the number of Model A’s and B represents the number of Model B’s. Now show your calculations to graph the equation 2X + 3Y < 18. Y l l 7l l 6l l 5l l 4l l 3l l 2l l 1l l___________________________________________ X
Paper For Above instruction The task involves constructing linear programming constraints based on manufacturing time limitations for different product models and graphing a linear inequality. Specifically, the problem presents the assembly and packaging times for two models—Model A and Model B—and asks to formulate constraints related to available hours in assembly and packaging departments, as well as to conceptualize the graph of the inequality 2X + 3Y < 18. First, translating the production times into constraints involves identifying the limit hours for each process. Given the data: Model A requires 1 hour for assembly and 0.5 hours for packaging. Model B requires 1.5 hours for assembly and 0.33 hours for packaging. To formulate the constraints for assembly hours, the total hours spent on both models must not exceed 800 hours: 1 * A + 1.5 * B ≤ 800 Similarly, for packaging hours, the total packaging time can't exceed 100 hours: 0.5 * A + 0.33 * B ≤ 100 These inequalities limit the feasible production levels of Model A and Model B based on the resource constraints. Next, regarding the inequality 2X + 3Y < 18, it can be analyzed as a linear boundary in a coordinate plane, where X and Y represent production quantities or related variables. To graph this, we identify the