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

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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

pic #2

 

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.

pic #3

 

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)

pic #6

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

 

piv#5

 

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.