You are the owner of a factory that makes widgets and gadgets. For each widget and...

   

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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. Az = b where A dictates how the features are combined, and b is the gold standard. However, realistically, it is too expensive to exactly satisfy Az = b, so you have to make some concessions. Instead, you can solve one of three optimization problems: minimize || Axb||1 = ax-bx| minimize || Ax - bl| = max|ax - bk| x minimize || Ax- - b||2 k = Vk arx - bk| (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. (1) (2) (3) 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. Az = b where A dictates how the features are combined, and b is the gold standard. However, realistically, it is too expensive to exactly satisfy Az = b, so you have to make some concessions. Instead, you can solve one of three optimization problems: minimize || Axb||1 = ax-bx| minimize || Ax - bl| = max|ax - bk| x minimize || Ax- - b||2 k = Vk arx - bk| (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. (1) (2) (3)