Question

What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below?

Answer 1

Answer:

P < 28

Step-by-step explanation:

given the constraints:

x + 2y < 10

y < 2

x>0

y>0

we can see that the range of y is from 0 to 2: $0$

we can use the maximum value of y in x+2y<10, to find the range of x

x + 2y < 10

x + 2(2) < 10

x < 10 -4

x < 6

now we know that range of x is from 0 to 6: $0$

take a closer look at these ranges, both of the ranges of x and y don't include their extreme values. (these are not $0\leq x\leq 6,\,\,0\leq y\leq 2$ )

The function P is:

P = 4x + 2y, we can easily put in all the maximum ranges of x and y in the equation to find the maximum value of P. but before plugging in the values we must be careful: we are putting the extremes of the ranges in the equation, but these extremes are not in the actual range itself.

so instead of writing that the maximum value of P is equal to a number, we should write that the maximum value of P is close to that number(or approaching that number from below)

P < 4(6) + 2(2)

P < 28

NOTE:

if the constraints given include the extremes of the ranges. Then the answer will be P = 28.

Answer 2

What are the constraints?


When you graph the constraints the four points you can use are (0,0), (10,0), (0,2), and (6,2). 

(10,0) is the point that gives you the maximum value which is 40.