Question

Which are the maximum values ? I will add a picture please help

Answer 1

58 at the point (9,8)

7 at the point (1, 1)

Explanation:

The maximum points will be found in the vertices of the region.

Therefore the first step to solve the problem is to identify through the graph, the vertices of the figure.

The vertices found are:

(1, 10)

(1, 1)

(9, 5)

(9, 8)

We look for the values of x and y belonging to the region, which maximize the objective function
`f(x, y) = 2x + 5y`. Therefore we look for the vertices with the values of x and y higher.

(1, 10), (9, 5), (9, 8)

Now we substitute these points in the objective function and select the one that produces the highest value for f (x, y)

`f(1, 10) = 2(1) + 5(10) = 52\\\\f(9, 5) = 2(9) + 5(5) = 43\\\\f(9, 8) = 2(9) + 5(8) = 58`

The point that maximizes the function is:

`(9, 8)` with
`f(9, 8) = 58`

Then the value that produces the minimum of f(x, y) is (1, 1)

`f(1, 1) = 2(1) + 5(1) = 7`