{"id":535,"date":"2024-12-12T08:00:00","date_gmt":"2024-12-12T07:00:00","guid":{"rendered":"https:\/\/control-advent.com\/?p=535"},"modified":"2025-11-28T19:05:46","modified_gmt":"2025-11-28T18:05:46","slug":"12-from-fragile-to-fantastic-optimising-toy-crafting","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=535","title":{"rendered":"12 – From Fragile to Fantastic: Optimising Toy Crafting"},"content":{"rendered":"\n

Authors of this question:<\/strong> Damiano Rotondo, Institutt for data- og elektroteknologi (IDE), <\/em>Universitetet i Stavanger, Norway & Helem S\u00e1nchez, Hafrsfjord Skole, Norway<\/p>\n\n\n\n

In Santa\u2019s bustling workshop, the elves are in full swing, crafting toys destined to delight children across the globe. Their secret to creating top-notch toys lies in three magical knobs on their machines, each controlling a crucial factor: fragility (how easily a toy breaks), unattractiveness (how unappealing the toy looks), and energy consumption (how much power the machine guzzles). The challenge? Turning down fragility and unattractiveness for sturdier, prettier toys makes energy consumption spike! It\u2019s a delicate balancing act, and the elves know they can’t bring all three to zero at once.<\/p>\n\n\n\n

Long ago, a brilliant mathematician named Jacopo Riccati paid a visit to Santa\u2019s workshop, leaving behind a gift that would transform toy-making forever: a magical formula. This enchanted equation, lovingly nicknamed Lovely Quality Reinforcement (or LQR by the elves), became the secret to perfecting the workshop’s machines. Whenever the elves tweak the knobs, they adjust the positive numbers a, b, c<\/em> in the formula:

J = a (fragility)2<\/sup> + b (unattractiveness)2<\/sup> + c (energy consumption)2<\/sup><\/em>

The LQR formula works like a charm, guiding the machines to find the optimal settings automatically. By balancing these tricky trade-offs, the formula ensures the minimal possible value of J<\/em>. Magical, isn’t it?

This year, a new challenge looms over Santa\u2019s workshop: soaring energy costs. With the magical machines working overtime and every watt counting, Santa knows he must act fast. If he doesn\u2019t keep energy use in check, it could jeopardize not only his gift deliveries but also the cherished future of the Control Advent Calendar! The stakes have never been higher.

Armed with Jacopo Riccati\u2019s magical formula, he wonders: how can he adjust the knobs to make energy savings the top priority?<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

a. \ud83d\udd27\ud83d\udc94\ud83d\udcc8 He should increase the parameter for fragility a<\/em><\/p>\n\n\n\n

b. \ud83c\udfa8\ud83d\udc40\ud83d\udcc8 He should increase the parameter for unattractiveness b<\/em><\/p>\n\n\n\n

c. \u26a1\ud83d\udd0c\ud83d\udcc8 He should increase the parameter for energy consumption c<\/em><\/p>\n\n\n\n

d. \u26a1\ud83d\udd0b\ud83d\udcc9 He should decrease the parameter for energy consumption c<\/em><\/p>\n\n\n\n

e. \ud83d\udcc8\ud83c\udf81\ud83c\udf1f He should increase all the parameters (a<\/em>, b<\/em>, and c<\/em>) at the same time<\/p>\n\n\n\n

f. \ud83e\udd8c\u2728\u2699\ufe0f He should sprinkle magical reindeer dust on the knobs<\/p>\n\n\n

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