Food Manufacture 1: When to Buy and How to Blend

The following constraints are used in this example:

bounds on decision variables
for $\text {period} \in \text {PERIODS}$ ,

$\Variable{Manufacture[period]} = \sum \limits _{\text {oil} \in \text {OILS}} \Variable{Use[oil,period]}$
for $\text {period} \in \text {PERIODS}$ ,

$\sum _{\text {oil} \in \text {VEG}} \Variable{Use[oil,period]} \le \Argument{veg\_ ub}$
for $\text {period} \in \text {PERIODS}$ ,

$\sum _{\text {oil} \in \text {NONVEG}} \Variable{Use[oil,period]} \le \Argument{nonveg\_ ub}$
for $\text {oil} \in \text {OILS and period} \in \text {PERIODS}$ ,

$\Variable{Store[oil,period}-1\Variable{]} + \Variable{Buy[oil,period]} = \Variable{Use[oil,period]} + \Variable{Store[oil,period]}$
for $\text {period} \in \text {PERIODS}$ ,

$\Argument{hardness\_ lb} \le \frac{\sum \limits _{\text {oil} \in \text {OILS}} \Argument{hardness[oil]}\cdot \Variable{Use[oil,period]}}{\Variable{Manufacture[period]}} \le \Argument{hardness\_ ub}$