Question

I was asking for HELP from people who do take PreCalc on connections academy but OKAY. -.-
Here's a question:
Which term best describes the solution of the situation represented by the system of inequalities? (Assume that x is greather than or equal to 0 and y is greater than or equal to 0)

3x+4y is less than or eaual to 8

2x+4y is less than or equal to 6
f(x,y)=x+y

A. alternate optimal solutions
B. One Optimal Solution
C. Unbounded
D. Infeasible

I don't understand this at all. Can someone please explain this to me?

Answer 1

never seen these words before, I would have to go look it up

Answer 2

is this business calculus?

Answer 3

No, it's standard PreCalc. I haven't either so I got really confused

Answer 4

are there any videos or definitions given to you at all in a book, online, etc?

Answer 5

The videos that I watched, no.

Answer 6

system of inequality is a region of solutions but in business they are important when making decisions about setting the lowest cost or making the maximum profit
sorry, I have to go now, maybe I will go look it up later in my precal books

Answer 7

is there something related to f(x,y) at the end? like f(x,y) = x+y = some value?

Answer 8

@ChelseaChiodos Anyways the answer according to me is, A.

Answer 9

no it was just f(x,y)= x+y.
Thank you

Answer 10

need explaination?

Answer 11

Could you explain why though? lol

Answer 12

Sure, have you done any type of such ques before?

Answer 13

Nope

Answer 14

See, these types of ques are better understood by plotting graphs;
the 4 given equations here are:
x greater than equal to 0
y greater than equal to 0
3x+4y is less than or eaual to 8
2x+4y is less than or equal to 6
So, first take these equations as:
x=0
y=0
3x+4y=8
2x+4y=6
And plot them on y-x graph.
Then try to understand that,
x greater than equal to 0 i.e. we will simply consider the region above x-axis
y greater than equal to 0 i.e. we will simply consider the region abv y-axis
Further, we will now consider the region in 1st quadrant
3x+4y is ''less than'' or eaual to 8
As u can see the line of 3x+4y=8, we will consider the region in 1st quad and below this line, as it is 'less than'
2x+4y is less than or equal to 6
As u can see the line of 2x+4y=6, we will consider the region in 1st quad, below previous line and also below this line as here also it is 'less than'.
(Also, u will need to calculate the intersecting point of these 2 lines for better understanding and plotting of graph)
Now observe, that there is a real region present for these conditions in the graph and also all the points in that region are real. So we have more than 1 values of x.y to satisfy these equations.
So ans is A.
Got it? :P

Answer 15

@ChelseaChiodos ^ try this, and you can do similar ques using this method.

Answer 16

Sorry, it took me awhile to reply I was e-mailing my teacher. Thank you very much I will try that out

Answer 17

np

Answer 18

@shanks is this linear programming and we are looking at the vertex?

Answer 19

sort of, the concept used in linear programming is somewhat similar.
Its just that in linear programming we find the optimal solution, specific solution to maximize or minimize something.
That's why in the beginning i asked about f(x,y) =x+y (it should be maximize this or minimize this)(in this case we will lookout for vertex method and further check for maximum or minimum value)
But in case there is no such thing, we need to lookout for the solution of these inequalities i.e. values of x and y. And by plotting graph(as in LP) we can see that there are many values of x,y that satisfy these conditions. That's my interpretation :P :)