Question

Use graphical methods to solve the linear programming problem.

2x + 6y ≥ 30.
4x + 2y ≥ 20.
x ≥ 0.
y ≥ 0.
Minimize P = 0.18x + 0.12y



A. Minimum of 1.86 when x = 9 and y = 2


B. Minimum of 1.08 when x = 4 and y = 3


C. Minimum of 1.02 when x = 3 and y = 4


D. Minimum of 1.2 when x = 4 and y = 4

Answer 1

I think it might be B. but i am not sure.

Answer 2

Do you try to solve first,
\[2x+6y=30\\
4x+2y=20\]?

Answer 3

I don't exactly understand how to do it.. :(
Why do you get 30 when you add 2x and 6y?

Answer 4

Well, you don't obtain 30, you can solve the system of equations.

Answer 5

Oh duh im sorry i totally just had a blonde moment.

Answer 6

Do you see the symbol ≥? That means that the equation from the left could be greater or equal to the number of the right.

However, this problems says it must be solved graphically. have you tried to plot the equations of the problem?

Answer 7

x = 15 - 3y
plug that in for x to solve for y

Answer 8

When you solve the system of equations, you obtain x=3, and y=4. But remember, you must select the minimum from the points of the graph.

Answer 9

So the answer is B?

Answer 10

The minimum as you see from the graph must be a vertex, just like one which is in x=3 y=4. Once you get the numbers, plug in into the formula,
\[P=0.18\cdot3+0.12\cdot 4=1.02\]And you get the answer.

Answer 11

Thank you both, i understand now.