Define the key components of linear programming: Provide a clear description of the decision variables, objective function, and constraints in plain language. Sample answer for Exercise Q$3$o Decision Variables: the number of x$-$pods and the number of BlueBerryso Objective functions: maximize the profito Constraints: $240$ hours of electronic time are available and $100$ hours of assembly department time are available$\mathrm{.}2.$ Formulate the Model: Write the linear programming model, including the objective function, constraints, and decision variables, in mathematical notation$3.$ Solve the Model: Graph the feasible region, identify the corner points, and determine the optimal solution manually.

Question $1$: Royce manages a printing office in Camarillo, using two types of machines: a high$-$speed printer and a binding machine. Each report requires $1\mathrm{.}5$ hours on the high$-$speed printer and $0\mathrm{.}5$ hour on the binding machine. Each brochure requires $1$ hour on the high$-$speed printer and $1$ hour on the binding machine. The high$-$speed printer is available for $20$ hours per week, and the binding machine is available for $24$ hours per week. Reports generate $$3$ in revenue each, while brochures generate $$5$ in revenue each. How many of each should Royce produce to maximize revenue? What is the maximum revenue?