Linear Programming (Algebra II):
An airliner has two types of planes, A&B. Plane A has 20 first class seats and 30 tourist class seats. It costs $1000 to hire a plane A and $1500 to hire a plane B. The senior class needs 160 first class seats and 300 tourist class seats for its annual Spring Break in the Bahamas. How many plane A's and how many plane B's should the seniors hire to get to the Bahamas at minimal cost?

So, my teacher explained the chart and graph method of solving this problem. I just keep getting an error for a response. I know it's an error because when I try to graph the shape I'm supposed to have four

Question

Linear Programming (Algebra II):
An airliner has two types of planes, A&B. Plane A has 20 first class seats and 30 tourist class seats. It costs $1000 to hire a plane A and $1500 to hire a plane B. The senior class needs 160 first class seats and 300 tourist class seats for its annual Spring Break in the Bahamas. How many plane A's and how many plane B's should the seniors hire to get to the Bahamas at minimal cost?

So, my teacher explained the chart and graph method of solving this problem. I just keep getting an error for a response. I know it's an error because when I try to graph the shape I'm supposed to have four

anonymous · Answer

vertices but I only have three.

anonymous · Answer

For constraints I got:
20x+20y is greater than or equal to 160
30x+30y is greater than or equal to 300
x is greater than or equal to 0
y is greater than or equal to 0

anonymous · Answer

For my objective function I got 1000x+1500y=p

anonymous · Answer

I have a quiz on this tomorrow so any explanation you can provide would be really helpful and greatly appreciated.

alienium · Answer

idk what you're trying to do
but to solve this you can simply put them in a system and try to solve them with substitution...
and from then you just pick the solutions that match the constrain

anonymous · Answer

An example please?

anonymous · Answer

Thanks for replying.

alienium · Answer

when you have like 2 equations...
say:
3x+4y=18
12x^2-3y=9
and you have to find the values that solve them both
you take x or y aside in one of the equations and substitute that expression in the other equation wherever you see that variable that you took aside in the first one.
like:
in the equation: 3x+4y=18 you take aside x for example
3x=18-4y
x=(18-4y)/3
now you substitute (18-4y)/3 everywhere there is an x in the other equation
>> 12[(18-4y)/3]^2-3y=9
now you solve the above equation... and that will give you Y
now you get the y value and place it in the first equation to get X
when you have them both, you have the pair of 2 numbers that solve both of the equations

anonymous · Answer

I understand. I love using substitution. I'm just not sure what equations I would be using to substitute.