Answer:
480 ...12%9 of 8000 ÷2...
You can use the substitution method.
You substitute the first equation to the second equation to get the value of x.
x + 3y = -14
x + 3(2x) = -14
x + 6x = -14
7x = -14
x = -14/7 = -2
Substitute the value of x to the first equation.
y = 2(-2) = 4
You can read it of the graph which is (1,3) or also calculate it with vectors:
calculate the vector CD:
(5-(-3),2-4)=(8,-2)
to calculate the midpoint you need half of the vector length:
(8,-2)/2=(4,-1)
add the vector to C:
(-3,4)+(4,-1)=(1,3)=midpoint of CD
so it's the third option
X+y<=20 is false, because it tries to correlate the amount of hats and scarfs with the time, without considering the time to knit each object
x<=5 is correct, he can at most make 5 hats for more he is missing yarn
y<=8 is correct, same reasoning but with scarfs
5x+8y<=20 is false, it compares the yarn requirements with the total time
12x+6y<=20 is correct, a corrected version of the first constraint which uses the worktime of each object essentially meaning "the time worked on all objects has to be less than the 20 hour time total"
so
x<=5
y<=8
12x+6y<=20
are correct
