10. (40 points) Please write your final answer or calculations as instructed. A local shop makes two main products: bookshelf and coffee table. They sell bookshelves for a profit of $50 each and coffee table for a profit of $70 each. Each booksheli takes 20 labor bours and each coffee table take 10 labor hours. It takes 15 board feet of lumber for each bookshelf and 20 board feet of lumber for each coffee table. Each week, there are only 120 labor hours and 140 board fect of lumber available. How many of each piece of fumiture should the shop make to maximize profit? Note: it's okay to have decimal places during calculation even though we covildn't make partial fiemiture practically. (a) Identify and label the decision variables and formulate the objective function and constraints. Decision variables: Objective function: Constraints: (b) Plot the constraints on the grid below and shade the feasible region and identify all possible cerner points (please label X and Y axes based on your decision variables). (c) Use either comer-point or iso profit/cost line method to find the optimal solution and the optimized value of your objective function. Optimal solution: Optimized value of your objective function