Owen would like to make a small income as an artist. Owen asked his friend Emily for advice about what combination of pictures to make. She suggested that he determine a reasonable profit for that month’s work and then paint what he needs in order to earn that amount of profit. • Each pastel requires $5 in materials and earns a profit of $40 for Owen. • Each watercolor requires $15 in materials and earns a profit of $100 for Owen. • Owen has $180 to spend on materials. • Owen can make at most 16 pictures. a. State the system of inequalities that represents this situation. Remember to define your variables and include any non-negative constraints that are required. b. What is the optimization equation? c. On graph paper, create this feasible region to use in this problem. Label your axes. d. Suppose Owen decided $1,000 would be a reasonable profit. Find three different combinations of watercolors and pastels that would earn Owen a profit of exactly $1,000. Mark these points on your graph. e. Now suppose Owen wanted to earn only $500 in profit. Find three different combinations of watercolors and pastels that will earn Owen a profit of exactly $500. Using a different-coloured pencil, add those points to your graph. f. Owen’s mother has convinced him that he should try to earn as much as possible. So, Owen needs to figure out the most profit he can earn within his constraints. He also wants to be able to prove to his mother that it is really the maximum amount. Find the maximum possible profit that Owen can earn and the combination of pictures he should make to earn that profit.​