- 2
- 55 Views
- All levels
![pumpkin1625 pumpkin1625](https://epin.tips/img/profile/p/pumpkin1625.jpg)
pumpkin1625
High School
Find the values of x and y that maximize the objective function P=3x+2y for the graph. What is the maximum value?
Leave an answer
Our People Answers
1
(Based on todays review)
-
tramserran
Here, we are required to find the a combination of the values of x and y that maximize the objective function; P=3x+2y.
The values of x and y are 9 and 0 respectively, i.e at point (9,0).
The maximum value of P, at this point is;
P = 27.
First, it is important to know that the point of maximisation (i.e the combination of values of x and y where the objective function is maximized) is usually given by the coordinate of a vertex.
- To find this point, there's a need to test all points given on the graph as follows;
For point (0,8):
- we have, P = 3(0) + 2(8)
- Therefore, P = 16.
For point (5,4):
- we have, P = 3(5) + 2(4)
- Therefore, P = 23
For point (9,0):
- we have, P = 3(9) + 2(0)
- Therefore, P = 27.
Therefore, the objective function is maximixed for values of x and y given by 9 and 0 respectively, i.e at point (9,0).
Therefore, the maximum value of P, at this point is;
P = 27.
Read more:
-
adioabiola
To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.
NOTE: I don't understand why (5,4) was given on your graph as a vertex.
(0,8): P = 3(0) + 2(8) = 0 + 16 = 16
(5,4): P = 3(5) + 2(4) = 15 + 8 = 23
(9,0): P = 3(9) + 2(0) = 27 + 0 = 27 THIS IS THE LARGEST (MAX) P-VALUE
Answer: 27
Recommend Questions
What is the volume of the rectangular prism. Type the answer in the boxes below
- November 2022
- 1
- Intermediate
why does obrien have winston arrested when obrien is the one who made first contact
- November 2022
- 3
- Intermediate