A, B, and C make handicrafts, bouquets and vases (a bouquet and a vase make a set). If A can make 10 bouquets or 11 vases per hour; B can make 11 bouquets or 12 vases per hour. vases; C makes 12 bouquets or 13 vases per hour, if they work together for 23 hours, how many sets can they make at most? Please tell us your plan and reasons.
甲、乙、丙三人制作工艺品，花束和花甁(一支花束和一个花瓶配成一套)若甲每小时能制作10支花束或11个花瓶；乙每小时能制作11支花束或12个花瓶；丙每小时制作12支花束或13个花瓶，若他们共同工作23小时，则最多可以制作出多少套？请说出你的方案及理由．
<gadget id="calculator">11 * 23</gadget>
<output>253</output>

<gadget id="calculator">12 * 12</gadget>
<output>144</output>

<gadget id="calculator">253 + 144</gadget>
<output>397</output>

<result>397</result>