Question

What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below? x+2y<_ 10. y<_2. x>_0. y>_0.

Answer 1

Answer:

The maximum value of P is $40$

Step-by-step explanation:

we have the constraints

$x+2y\leq 10$ ------> constraint A

$y\leq 2$ ------> constraint B

$x\geq 0$ ------> constraint C

$y\geq 0$ ------> constraint D  

$P=4x+2y$

Using a graphing tool

The solution of the constraints is the shaded area in the attached figure

For the point $(0,0)$

The value of P is equal to

$P=4(0)+2(0)=0$

For the point $(6,2)$

The value of P is equal to

$P=4(6)+2(2)=28$

For the point $(0,2)$

The value of P is equal to

$P=4(0)+2(2)=4$

For the point $(10,0)$

The value of P is equal to

$P=4(10)+2(0)=40$

therefore

The maximum value of P is $40$

Answer 2

The answer is D. 40. I hope this helps!!!!!