Question: Set up, but do not solve the following problem. A factory manufactures two types of gadgets, regular and premium. Each gadget requires the use of

Set up, but do not solve the following problem.

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 12 hours available each day for each operation. A regular gadget requires 1 hour of assembly and 2 hours of finishing, while a premium gadget needs 2 hours of assembly and 1 hour of finishing. Due to other restrictions, the company can make at most 7 gadgets a day. If a profit of $20 is realized for each regular gadget and $30 for each premium gadget, how many of each type of gadget should be manufactured each day to maximize profit?

x:=the number of regular gadgets manufactured

y:=the number of premium gadgets manufactured

P:=the manufacturer's daily profit (in dollars)

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