# Thread: Solve word prob using linear inequalities??

1. ## Solve word prob using linear inequalities??

You are the manager of a small appliance store. You need to order two types of microwave ovens. The deluxe model costs you $500 and the basic model costs you$300. The profit for the deluxe model is $200 while the profit for the basic model is$50. You would like to sell a minimum of 100 microwaves and make a total profit of at least $8000. How many of each model should you order to minimize the costs? 2. Originally Posted by katt You are the manager of a small appliance store. You need to order two types of microwave ovens. The deluxe model costs you$500 and the basic model costs you $300. The profit for the deluxe model is$200 while the profit for the basic model is $50. You would like to sell a minimum of 100 microwaves and make a total profit of at least$8000. How many of each model should you order to minimize the costs?
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.

3. Originally Posted by 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.
also can you tell me how to place it in an linear inequality for final answer? an linear inequality equation for graphing the solution also?