Find the ordered pair where the maximum value occurs for the equation C = 12x – 4y given the following constraints:

Question

smarty · Answer

$$y \ge4$$
$$x \ge1$$
$$x+2y$$
$$y-x \le5$$

smarty · Answer

@zepp

anonymous · Answer

is it just x+2y?

smarty · Answer

$$x+2y \le16$$

anonymous · Answer

better...

anonymous · Answer

from that we get$$y \ge4,y \ge (12-C)/4,y \le 8-x/2, y \le 5+x$$
intersecting, 8-x/2=5+x -> x=2,y=7 ,C=24-28=-4

anonymous · Answer

y=4, y=8-x/2 ,y=5+x

anonymous · Answer

intersecting 8-x/2=4 -> x=8, y=4 ,C=8*12-16=80

anonymous · Answer

intersecting 5+x=4 -> x=-1,y=4 -> C=-12-16=-28
Thus, answer is C=80

anonymous · Answer

Just to check if c=80 is valid, y>= (12-c)/4, c=80, y=4 'ok'

smarty · Answer

A.(1, 4)
B.(2, 7)
C.(8, 4)
D.(10, 1)

anonymous · Answer

(2,7) -> c=80

smarty · Answer

hmk. Thanks.

anonymous · Answer

you plot those 3 eq, that will get u a triangle,
find those vertices and plug the values into C, see which one has the higher value, double check if C is valid and that's it.

smarty · Answer

Alright, i'll do that on my grapghin calc

anonymous · Answer

you should get this triangle,