Woodco manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 180 board feet of oak and 280 board feet of pine are available. A table requiere either 18 board feet of oak of 30 board feet of pine; and a chair requires either 6 board feet of oak or 14 board feet of pine. Each table can be sold for $45 and each chair for $18. Since most customers buy tables and chairs at the same time( but not necessarily made from the same wood). Woodco has decided that the ratio of chairs to tables should be at least 2 and at most 8. How many tables and chairs of each type should woodco manufacture to maximize revenues. Using mathematical symbols, formulate this problem as a linear programming model.
a) Define the decision variables b) specify the objective function c) Write the constraints (using inequalities) including the non negativity statement.