The Outdoor Furniture Corporation manufactures two products, benches andpicnic 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 productioncycle, 1,200 hours of labor are available under a union agreement. The firm also has astock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture producesrequires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35feet of redwood. Completed benches will yield a profit of $9 each, and tables will result ina profit of $20 each.

a) Formulate this as Linear Programming (LP) problem by showing the mathematical expressions for the objective function and the constraints. 

b) Use the graphical solution, show the feasible region for this problem 

c) Use the corner point graphical approach, how many benches and table should Outdoor Furniture produce to obtain the largest possible profit? 

d) How much would earnings increase if the stock of good-quality redwood change from 3,500 to become 5,000 feet?