A chair manufacturer makes three different types of chairs, each of which must go through sanding, staining, and varnishing. In addition, the model with vinyl-covered back and seat must go through an upholstering process. The following table gives the time required for each operation on each type of chair, the available time for each operation in hours per month, and profit per chair for each model. How many chairs of each type should be made to maximize the total profit? Model Sanding Staining Varnishing Upholstering Profit (hours) (hours) (hours) (hours) (J.D.) Solid back and seat 1.0 0.5 0.7 0 10 Ladder back, solid 1.2 0.5 0.7 0 13 seat Vinyl-covered back 0.7 0.3 0.3 0.7 8 and seat Total time available 600 300 300 140 per month (a) Set up a linear programming model for this situation. (b) Solve the model. (c) Perform a sensitivity analysis on the model. (d) Comment on the solution, noting the meanings of the slack variables and the ranges for resource and cost components. 00