a. Let x represent the number of pastels and y represent the number of watercolors that Owen makes.
The system of inequalities representing this situation can be written as:
5x + 15y ≤ 180 (constraint on materials cost)
x + y ≤ 16 (constraint on the number of pictures)
x ≥ 0, y ≥ 0 (non-negative constraints)
b. The optimization equation is to maximize the profit, which can be represented as:
Profit = 40x + 100y
d. To find three different combinations of watercolors and pastels that would earn Owen a profit of exactly $1,000, let's substitute the profit value into the optimization equation and solve the system of inequalities:
Profit = 40x + 100y = 1000
First combination:
40x + 100y = 1000
Solving with the constraints, we can substitute x = 2 and y = 8 to get:
40(2) + 100(8) = 80 + 800 = $880 profit
Second combination:
40x + 100y = 1000
Solving with the constraints, we can substitute x = 4 and y = 6 to get:
40(4) + 100(6) = 160 + 600 = $760 profit
Third combination:
40x + 100y = 1000
Solving with the constraints, we can substitute x = 6 and y = 4 to get:
40(6) + 100(4) = 240 + 400 = $640 profit
1. 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.
1 answer
1 answer