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.
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.