Question

Inequality help please? I'll give a medal!

Answer 1

The first attachment is the problem, and the second is the graph I made of the inequalities.

Answer 2

We need the points of intersection of the three lines.
If you click on the intersection points it will tell you the coordinates.

Answer 3

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Answer 4

\(f(x,y) = 5x + 4y\)
Points of intersection: \((3,5); ~~(5,3); ~~(9,7) \)
Find: \(f(3,5); ~~ f(5,3); ~~ f(9,7)\).
Whichever gives the lowest value if the minimum value of \(f(x,y)\).

Answer 5

(3,5).... 5(3) + 4(5) = 15 + 20 = 35
(5,3).... 5(5) + 4(3) = 25 + 12 = 37
(9,7).... 5(9) + 4(7) = 45 + 28 = 73

(3,5) gives us the minimum value.

Answer 6

Problem is - that coordinate isn't an option.

Answer 7

let me check if there were any typos when I typed the inequalities for graphing.

Answer 8

No typos. But the points in the answer choices b, c and d are not even in the solution space. Only points in the within the triangle and on the sides of the triangle satisfy the given inequalities. The point in a) (5,3) is the ONLY ONE that belongs in the solution space. So it is the only choice for an answer. But it is NOT the absolute minimum. Point (3,5) gives real minimum but since it is not one of the choices we cannot choose that point.

Answer 9

That is the problem I ran into. I'm just glad to see that I'm not the only one having that issue.

Answer 10

Well it said the answer was correct, but I'm not sure why it didn't have the right coordinate. O.o

Answer 11

Probably a typo in the answer. They probably mean to type (3,5) but typed (5,3). It happens sometimes in books and online course work.

Answer 12

Yeah that's I thought, but thank you for your help. ^^