A concrete company makes three kinds of mixtures. They can sell up to 400 tons of each mixture at the following prices (per ton): mixture A, $100; mixture B, $120; mixture C, $210. The company purchases raw material at $50 /ton. Each ton of raw material can be used to produce either 1 ton of mixture A or 1 ton of mixture B. For a cost of $30 /ton processed, mixture A can be converted to .6 tons of mixture B and .4 tons of mixture C. For a cost of $22 /ton processed, mixture B can be converted to .75 tons of mixture C. Formulate a linear program (with clearly defined decision variables and constraints) that maximizes the company's profit. Hint: you will need the following seven decision variables. 1. The net number of tons of mixtures A,B and C produced ( 3 variables) 2. The number of tons of mixtures A and B produced from raw materials ( 2 variables) 3. The number of tons of mixture A processed (to obtain other mixtures) (1 variable) 4. The number of tons of mixture B processed (to obtain other mixtures) (1 variable) Solve your model from Part 1 using Gurobi/Python. Your program should include output that shows the optimal solution and optimal objective value