A company gets three byproducts A, B and C, in quantities of 6000, 10,000, and 5000 tons, respectively/month from the manufacturing process of their main product. The company can make a fertilizer consisting of 30% of A, 50% of B, and 20% of C and sell it at a profit $5/ton. They can also make a construction material consisting of 40% of A, 30% of B, and 30% of C and sell it at a profit $4/ton. Any leftover quantities of A,B, and C can be given away to a company dealing with bulk materials.

(1.1) Formulate a linear optimization model to find a plan that maximizes the profit of the company by using these three byproducts and use the primal simplex method to solve the LO model

(1.2) In a specific month, due to some disruption in the production process, the company finds that the amount of byproduct B reduces to 8000 tons. Find the optimal plan for the company in such a month.

(1.3) Based on recent market information, the company finds that the demand for the fertilizer is reduced to 15,000 tons. What is the new optimal plan for the company?

(1.4) The bulk material handling company (BMHC) developed a new plan to make fertilizer and construction material using the byproducts A, B and C. The BMHC wishes to force the manufacturing company to stop making fertilizer and construction material from their byproducts. Please find the optimal pricing strategy for BMHC to minimize its overall cost. Solve using Sensitivity Analysis and also use primal simplex method to solve the linear programming