is this correct for part a: To formulate the linear programming model, we need to define the decision variables, the objective function, and the constraints. Decision variables: x1: number of units of product 1 produced x2: number of units of product 2 produced x3: number of units of product 3 produced Objective function: Maximize the total profit = 50x1 + 20x2 + 25x3 Constraints: Milling machine capacity constraint: 9x1 + 3x2 + 5x3 500 Lathe capacity constraint: 3x1 + 4x2 350 Grinder capacity constraint: 5x1 + 2x3 150 Sales potential constraint for product 3: x3 20 Non-negativity constraints: x1, x2, x3 0 The linear programming model can be written as: Maximize 50x1 + 20x2 + 25x3 Subject to: 9x1 + 3x2 + 5x3 500 3x1 + 4x2 350 5x1 + 2x3 150 x3 20 x1, x2, x3 0 To identify the basic solutions, we can use graphical analysis. The feasible region is defined by the intersection of the constraints. The basic solutions are: (0, 0, 0) - Infeasible (0, 87.5, 0) - Feasible (55.56, 0, 0) - Feasible (0, 0, 75) - Feasible The basic solutions are the extreme points of the feasible region. The first solution, (0, 0, 0), is infeasible because it violates the sales potential constraint for product 3. The other three solutions are feasible