Note: An LP formulation stands for a linear programming formulation and uses the decision variables to maximize the total profit plus the total inventory asset value.

PRACTICE QUESTION A chemical company mines phosphate rock, collects in inventory poles i = 1, ..., 8 and blends it to meet contracts with customers k = 1,..., 25. The critical measure of phosphate content in rock is its BPL (bone phosphate of lime). Piles correspond to different average BPL content b; per ton, asset value a; per ton, contract net profit rik per ton, starting inventory h; and expected quantity qi to arrive from mines vary accordingly. Each contract includes a minimum of skand maximum -Sk number of tons to be shipped, along with a minimum pk and maximum of "pkaverage BPL content. Managers want to schedule blending and sales to maximize total profit plus total inventory asset value. Formulate an LP formulation for this planning problem. Write down your assumptions in modeling, if any. Clearly state the definitions/meanings of your decision variables, objective function, and constraints