**I **.**Do Now: read the following problem. https://www.desmos.com/calculator/ecnyow98r1**

Marry has decided to plants some flowers, so she can make packet money. She will spend up to $180 for the seeds. One rose seeds cast $15, one peony seeds cost $5. She has enough space for plant 16 flowers. She wants to plants at lest 3 peonies and at lest 8 roses. If peonies earn$40 for her and the roses earn $60. how many of each type should marry to plant to maximize the amount of packet money she can make?

1. From the problem, list all the constraints:

- She will only spend up to $180 for the seeds.
- she has space only for 16 flowers.
- she wants plant at lest 3 peonies and 8 roses

2. Find variables:

let x = # of roses and let y = # of peonies

**II. Use Desmos to solve the problem by turning all the constraints into Inequalities.**

1. Turn the first two boxes of Desmos Graphing Calculator into a text boxes.

Type in our variables x = # of roses and let y = # of peonies

2. Turn the all constraints into inequalities and type then into the boxes of Desmos Graphing Calculator.

- 15x + 5y ≤ 180
- x + y ≤ 16
- y ≥ 3
- x ≥ 8

3. Turn everything into same color, that will make the region that we’re looking for a little bit more clear, because it just the darkest region.

4. The four sets of intersection of the darkest region are the sets that satisfied of our constraints.

- (10,6)
- (11,3)
- (8,3)
- (8,8)

**III. Solve the problem by set up a function with two variables x and y.**

- f(x,y) = x(60) + y(40)
- Plug the four sets into the function.

- f(10,6) = 840
- f(11,3) = 780
- f(8,3) =600
- f(8,8) = 800

**IV. Conclusion :**

As you can see when x = 10 and y = 6, Marry can make the maximum of money $840. So she should plants 10 roses and 6 peonies.

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