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**Unenlightened** Say you buy D deluxe models and B basic models.

You want to sell at least 100 microwaves, so $\displaystyle B+D \geq 100$

Your profit is at least 8000 so $\displaystyle 50B + 200D > \geq 8000$

These simultaneous equations give $\displaystyle D \geq 20, B \geq 80$.

So in order to satisfy both conditions, you must sell at least 20 deluxe models and 80 basic models. But since you are asked to minimize the cost, we shall assume you are not to sell any more than that. So you should sell 20 deluxe models and 80 basic models.