(Solved): - You can work individually or in pairs. Only 1 group member should submit the work to Moodle. Speci ...

- You can work individually or in pairs. Only 1 group member should submit the work to Moodle. Specify the group members in your submission. - Show your work to receive full credit. Late submissions will not be graded. GreenBuild Supplies produces eco-friendly furniture and makes two products: Eco Chairs and Eco Benches. Production is limited by available labor in two areas: woodworking and painting. - Eco Chair: - Requires 3 hours of woodworking. - Requires 1 hour of painting. - Generates a profit of \( \$ 20 \) per chair. - Eco Bench: - Requires 2 hours of woodworking. - Requires 3 hours of painting. - Generates a profit of \( \$ 40 \) per bench. In addition, demand considerations require that the company produce at least twice as many Eco Chairs as Eco Benches in any production run. The company has 120 hours of woodworking labor and 90 hours of painting labor available each week. GreenBuild Supplies wants to determine how many chairs and benches to produce each week to maximize profit. Part A: a) Formulate a linear programming model to maximize profit. Clearly identify the decision variables and constraints. b) Find the optimal solution and optimal objective function value using the graphical solution approach. Clearly indicate the feasible region and the constraints. c) Determine the types of constraints (i.e., binding, nonbinding, redundant). d) How many hours of woodworking and painting labor will remain unused if the optimal numbers of chairs and benches are produced? Part B: a) Determine the sensitivity ranges for the unit profits of Eco Chairs and Eco Benches. b) Using the sensitivity ranges you found in part (a), determine the new optimal solution and objective function value if the profit of an Eco Chair increases from \( \$ 20 \) to \( \$ 40 \). c) Using the sensitivity ranges you found in part (a), determine the new optimal solution and objective function value if the profit of an Eco Bench decreases from \( \$ 40 \) to \( \$ 10 \). d) Determine the sensitivity ranges for the right-hand sides of the woodworking and painting constraints. e) Determine the shadow prices for the woodworking and painting constraints. Answer the following parts considering the sensitivity ranges and shadow prices you found in parts (d) and (e). Do not solve the model again. f) What would be the effect of increasing the amount of available woodworking labor to 130 hours on the optimal solution and objective function value? g) What would be the effect of increasing the amount of available woodworking labor to 150 hours on the optimal solution and objective function value? h) What would be the effect of decreasing the amount of available painting labor to 80 hours on the optimal solution and objective function value?