Picturing Pictures

Hassan is an artist who specializes in geometric designs. He is getting ready for a street fair next month. He paints both watercolors and pastels, taking about the same amount of time to paint each one.

·  He decides he has time to paint a total of at most 16 pictures.

·  The materials for each pastel will cost him $5.

·  The materials for each watercolor will cost him $15.

·  He has $180 to spend on materials.

·  Each of these things is called a constraint.

Let x = the number of pastels and

y = the number of watercolors.

1. Write an inequality to represent each constraint.

Number of Pictures / Materials

Hassan makes a profit of $40 on each pastel and a profit of $100 on each watercolor.

2. Write an equation to represent his profit. This is called the objective equation.

Profit = ______

3. Make a graph that shows Hassan’s feasible region; that is, the graph should show all of the combinations that satisfy his constraints. Be sure you label the axes.

4. Suppose Hassan decides $1000 would be a great amount to make.

Find three different combinations of watercolors and pastels that would make him a profit of exactly $1000. Mark these three number pairs on your graph.

5. Now suppose Hassan decides that of $600 would still be a good amount to make.

Find three different combinations of watercolors and pastels that would make him a profit of exactly $600. Mark these three number pairs on your graph.

6. Finally, Hassan decides that if he could make just $500 he would still be happy.

Find three different combinations of watercolors and pastels that would make him a profit of exactly $500. Mark these three number pairs on your graph.

7. Hassan’s mother appeared on the scene and she thinks that he should try to earn as much as possible.

Hassan wants to figure out the most he can make within his constraints, AND, he wants to be able to prove to his mother that it is really the most.

Find the maximum possible profit that he can make and what combination of picture he should make to earn that profit.

Source: Baker’s Choice Unit, IMP