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.

1.   f(x,y) = x(60) + y(40)
2. 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.

https://www.desmos.com/calculator/cpujloxeyw