Swift Chemical Company23 mines phosphate rock, collects it in inventory piles i = 1,c, 8, and blends it to meet contracts with customers k = 1,c, 25 at profit pik per ton.

The critical measure of phosphate content in rock is its BPL. Piles correspond to different average BPL contents bi per ton, asset value ai per ton, contract net profit ri, k per ton, starting inventory hi, and expected quantity qi to arrive from mines vary accordingly. Each contract includes a minimum sk and a maximum sQ k number of tons to be shipped, along with a minimum pk and a maximum pQ k average BPL content. Managers want to schedule blending and sales to maximize total profit plus total ending inventory asset value. Formulate an LP model of this phosphate planning problem using the decision variables 1i = 1,c, 8; k = 1,c, 252 xi,k ! tons of rock from pile i included in shipment for contract k hi ! ending inventory in pile i