please add excel formulas and calculations.

Problem 1 The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 board feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 board feet of redwood; each picnic table takes 6 labor hours and 35 board feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each. Outdoor Furniture needs to decide how many benches and tables they should produce to obtain the largest possible profit. Define the decision variables necessary for the LP formulation as follows: X= number of benches produced Y= number of tables produced (a) Formulate appropriately as a profit maximization LP. Provide the algebraic model formulation in your submission. Must be neatly presented. (b) Input and solve the formulation using Excel. After running Solver, generate sensitivity report. Report how many benches and tables the firm will produce, and what is the maximum profit the firm can obtain