A contractor is considering two gravel pits from which he may purchase material to supply a project. The unit cost to load and deliver material to the project site is $5 per m3 from pit 1 and $7 per m3 from pit 2. He must deliver a minimum 10,000 m3 to the site.
The mix that he delivers must consist of at least 50% sand, no more than 60% gravel and no more than 8% silt. The material at pit 1 consists of 30% sand and 70% gravel. The material at pit 2 consists of 60% sand, 30% gravel and 10% silt.

i. Formulate LP model.

ii. Determine optimum solution by graphical method.

iii. Determine active and inactive constraints for the optimum solution.

iv. Determine the proportions of sand, gravel and silt in the optimum solution.