2. Robust optimization You are the owner of a factory that makes widgets and gadgets. For each widget and gadget, there is a set of feature measurements, e.g. the weight, dimensions, material composition, etc, packed in a vector x. For maximum profit, you want the combinations of these features to exactly match a set of gold standard specifications, e.g. Ax -b where A dictates how the features are combined, and b is the gold standard. However, realistically, it is too expensive to exactly satisfy Ax = b, so you have to make some concessions. Instead, you can solve one of three optimization minimize |A b1-> a^-bk minimize IA-?-max la[c-bel minimize IAT (a) Show that (1) is a linear program by writing it in standard LP form. (b) Show that (2) is a linear program by writing it in standard LP form. 2. Robust optimization You are the owner of a factory that makes widgets and gadgets. For each widget and gadget, there is a set of feature measurements, e.g. the weight, dimensions, material composition, etc, packed in a vector x. For maximum profit, you want the combinations of these features to exactly match a set of gold standard specifications, e.g. Ax -b where A dictates how the features are combined, and b is the gold standard. However, realistically, it is too expensive to exactly satisfy Ax = b, so you have to make some concessions. Instead, you can solve one of three optimization minimize |A b1-> a^-bk minimize IA-?-max la[c-bel minimize IAT (a) Show that (1) is a linear program by writing it in standard LP form. (b) Show that (2) is a linear program by writing it in standard LP form