In this lesson, you will apply either graphing or checking algebraically to determine if the solutions are reasonable.

San Jose, California, located south of San Francisco, is California's third largest city. It is also where the largest outdoor flea market is located in the United States. The San Jose Flea Market is located on 120 acres of land with eight full miles of paths with street signs. It is a maze of diverse merchandise; everything is available at the San Jose Flea Market.

Source: Visiting the market, Google

Hector and Carla asked their uncle if he would allow them to sell designer dresses in his shop at the market. Their uncle agreed to their opening a designer dresses in his shop at the market, but they have to pay him $512 per month to help offset his costs of running his shop. 

Besides paying their uncle they also had to purchase the designer dresses. The cost of each designer dress is $13. Therefore, Hector and Carla have the cost function, where C(x) is the total cost of running their shop. The 512 is the cost or dollar amount they have to pay their uncle for using his shop, the 13 is the cost or dollar amount of one dress, and x is number of dresses sold.  In this case, cost means the dollar amount they have to spend in order to run their business.

After researching their competition, Hector and Carla decide they can sell their dresses for $45 each. This gives them the revenue function in which R(x) is revenue, or the dollar amount they intend on receiving from the dresses sold. 45 is the dollar amount they anticipate selling the dresses for, and and x is number of dresses sold.  Revenue is the economic term for money they make from selling dresses.

To decide if they should enter the market business, Hector and Carla need to determine if they can make a profit.  To make a positive profit, they need their revenue to be greater than their costs.  In economics, the equation is: profit = revenue – cost.

They decided to graph their cost and revenue functions and find they intersect at (16, 720).

Determine whether the following statements are true or false?

1. If they sell 0 dresses, they will still have $512 in costs.
   
   
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   Check Your Answer

   True!
   
   
   
2. If they sell 3 dresses, they will make a positive profit.
   
   
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   Check Your Answer

   False.


3. If they sell 20 dresses, they will make a positive profit.
   
   
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   Check Your Answer

   True!
   
   
   
4. What is significant about the value 16 in the solution (16,720)?
   
   
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   Check Your Answer

   If they sell 16 items, they will break even; their revenue and costs are the same. If they sell more than 16 items, their revenue becomes greater than their cost, and they will earn a positive profit.


5. What is significant about the value 720 in the solution (16,720)?
   
   
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   Check Your Answer

   If they sell 16 items, their monthly cost and monthly revenue will both be $720.