1. Solve the following Linear Programing Model using Excel Solver The Luzon Timber Corporation cuts raw timber, lauan, and tanguile, into standard size planks. Two steps are required to make these planks from raw timber: debarking and cutting. Each hundred feet of lauan takes 1 hour to Each hundred feet of tanguile takes 1.5 hours to debark and 0.6 hours to cut. The bark removing machines can operate up to 600 hours per week but the cutting machines are limited to 480 hours per debark and 1.2 hours to cut. week. Luzon Timber can buy a maximum of 36,000 feet of raw lauan and 32,000 feet of raw tanguile. If the profit per hundred feet of processed logs is P180 for lauan and P200 for tanguile, how much lauan and tanguile should be bought and processed by the corporation to maximize total profits? Formulate this problem as a linear programming model.

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A farmer has 800 meters of fencing and needs to fence off a rectangular paddock that borders a straight river. He doesn't need to fence along the river. Set up and solve an appropriate optimisation problem to find the dimensions of the paddock that has the largest area.