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## what is the maximum value of p = 4x + 2y, given the constraints on x and y listed below? 10 20 24 40

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:

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:

take a closer look at these ranges, both of the ranges of x and y don’t include their extreme values. (these are not )

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.

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