Question: In given Example, we considered a single-period blending problem with limited availability of raw materials. In practice, we should account for the possibility of purchasing raw materials at a time-varying cost and storing them.

• Extend the model to a multiperiod decision model with purchase decisions, assuming that you know the future prices of raw materials and that storage capacity is unlimited. (Note: of course, assuming that future prices are known may be unrealistic; however, commodity derivatives could be used to eliminate uncertainty.)

• Assume that raw materials must be stored in separate tanks, which are available in a limited number. Hence, you may only store up to a given number of raw material types. How can you model this additional constraint?]

Example: (Optimal mix in a process industry) Let us write an optimal mix model suited for process industries, whereby the blend of raw materials to produce end items features some recipe flexibility.