A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 15,000 board feet of oak and 21,000 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair requires either 5 board feet of oak or 13 board feet of pine. Each table can be sold for $800, and each chair for $300.

a. Determine how the company can maximize its revenue.

b. Use SolverTable to investigate the effects of simultaneous changes in the selling prices of the products. Specifically, see what happens to the total revenue when the selling prices of oak products change by a factor 1 + k₁ and the selling prices of pine products change by a factor 1 + k₂. Revise your model from the previous problem so that you can use SolverTable to investigate changes in total revenue as k₁ and k₂ both vary from 20.3 to 0.3 in increments of 0.1. Can you conclude that total revenue changes linearly within this range?