A company cuts raw timber- mahogany and oak logs into wooden boards. Two steps are required to produce boards from the logs. The first step involves removing the bark from the logs. Two hours are required to remove bark from 1000 feet of mahogany and three hours per 1000 feet of oak logs. After the logs have been debarked, they must be cut into boards. It takes 2.4 hours for cutting 1000 feet of mahogany and 1.2 hours for cutting 1000 feet of oak logs. The bark removing machines can operate up to 60 hours per week while the cutting machines are limited to 48 hours per week. The company can buy a maximum of 18000 feet of raw mahogany logs and 12000 feet of raw oak logs per week. The profit per 1000 feet of processed logs is kshs 2800 and kshs 2000 for mahogany and oak respectively.

1. Formulate this problem as a linear programming problem.

Optimize the LP problem