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Find the maximum value of
C = 3x + 2y
Subject to the following constraints:
x > 0
y>0
x + 3y <15
4x + y <16
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Answer 1

Answer:

Given:

x > 0

y > 0

And,

x + 3y < 15

4x + y < 16

<=>

4x + 12y < 60

4x + y < 16

<=>

11y < 44

<=> y < 4

Otherwise

x + 3y < 15

4x + y < 16

<=>

x + 3y < 15

12x + 3y < 48

<=>

11x < 33

<=>

x < 3

=> C = 3x + 2y < 3*3 + 2*4 = 9 + 8 = 17

=>  C < 17

Hope this helps!

:)

Answer 2

The maximum value of  C is an illustration of objective functions

The maximum value of C is 25

The objective function is given as:

$\mathbf{C = 3x + 2y}$

The constraints are:

$\mathbf{x + 3y < 15}$

$\mathbf{4x + y < 16}$

$\mathbf{x,y > 0}$

Plot the graphs of the constraints

From the graph (see attachment), the only optimal point is (3,4)

Substitute 3 for x and 4 for y in the objective function.

So, we have:

$\mathbf{C = 3x + 2y}$

$\mathbf{C = 3(3) + 2(4)}$

$\mathbf{C = 9 + 8}$

$\mathbf{C = 17}$

Hence, the maximum value of C is 17

Read more about optimizing functions at:

https://brainly.com/question/14778650