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