A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of two operations, assembly and finishing, and there are at most $120$ hours available for each operation. A regular gadget requires $1$ hour of assembly and $2$ hours of finishing, while a premium gadget needs $3$ hours of assembly and $1$ hour of finishing. Due to other restrictions, the company can make at most $70$ gadgets a week. If a profit of $\$20$ is realized for each regular gadget and $\${}30$ for a premium gadget, how many of each should be manufactured to maximize profit each week? Enter the ordered pair $(x,y).$

 Aug 1, 2023

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