Question

Please help me solve this?
Chase Quinn wants to expand his cut-flower business. He has 12 additional acres on which he intends to plant lilies and gladioli. He can plant at most 7 acres of gladiolus bulbs and no more than 11 acres of lilies. In addition, the number of acres planted to gladioli (G) can be no more than twice the number of acres planted to lilies (L). The inequality L+2G>=10 represents his labor restrictions. If his profits are represented by the function f(L,G) = 300L + 200G, how many acres of lilies should he plant to maximize his profit?


I know this:

L <= 11
G <=7
L + 2G >= 10

And of course, his profit is represented by 300L + 200G.

I'm trying to figure this out, it's the last math question I have to do tonight and I just can't get it. Usually these are easy for me. Thanks in advance.

Answer 1

Graph it.

Answer 2

Shade what is true then.

Answer 3

I graphed those, and then remembered that the acres cannot be more than 12. I came up with 11 acres of lilies.

Answer 4

I'm not sure if that's right or if I should regraph with the equation L + G <= 12.

Answer 5

Regraph... is this algebra 2?

Answer 6

Precalc.

Answer 7

The vertices I got from regraphing are

(-4,7)
(5,7)
(11,1)
(11,-.5)

x values being the lilies and y values being the gladioli.

Answer 8

So either way, the max value of lilies for the best profit is 11.

Answer 9

Oh vadda vaddda i have IB math, is that similar to pre-calc?

Answer 10

I'm not sure.