Question

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?
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. (3 marks)
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.