SOLUTION: Linda williams has just begun a nusery business and seeks your advice. She has limited funds to spend and wants to stock two kinds of fruite-bearing plants. She lives in the northe

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Question 147092: Linda williams has just begun a nusery business and seeks your advice. She has limited funds to spend and wants to stock two kinds of fruite-bearing plants. She lives in the northeastern part of Texas and thinks that blueberry bushes and peach trees would sell well there. Linda can buy blueberry bushes from a supplier for $2.50 each and young peach trees for $5.50 each. She wants to know what combination she should buy and keep her outlay to $500 or less. Write an inequality and draw a graph to depict what combinations of blueberry bushes and peach trees she can buy for the amount of money she has. explain the graph and her options.
I know this is a long question but I am so confused with it. Can someone please help?
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let = number of blueberry bushes bought
Let = number of peach trees bought

You can plot on the y-axis and on the x-axis
First get the equation into the form
where is the slope and is the y-intercept
(just think of it as an equality for now)

Now I can plot this line
Remember, is the y-axis and is the x-axis

Any point that is within the triangle formed by the axes
and the line will satisfy
I'll pick a point to check.
It looks like and falls inside
the triangle. Now I substitute

This is true. Try another point to check. This may not be the
only way to graph it, but I think its a good way.

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!
Let x = the number of blueberry bushes
Let y = the number of peach trees

The amount of money she will spend on the bushes is 2.50x
The amount of money she will spend on the trees is 5.50y

The total amount she has to spend is 500, so the amount she spends on bushes plus the amount she spends on trees has to be less than or equal to 500.

Graph . Since your original inequality includes 'or equal' make your graph a solid line.

Now, pick a point that is NOT on the line you just graphed. Since the line does not go through the origin, the point (0,0) is a good choice because it makes the arithmetic easy.

Substitute the coordinate values for the point you chose into the original inequality and do the arithmetic. If the result is a true statement, shade in the half-plane containing the point you selected. If the result is false, shade in the other side of the line. In the case of your problem the result will be true, so the shaded area does, in fact, contain the origin (0,0).

For your problem, in practical terms, you also have other constraints, namely: and . That's because she can't buy a negative number of either bushes or trees. Therefore, you are only concerned with that part of your shaded area that is in the first quadrant of the coordinate system.

What this first quadrant shaded area represents is the area of feasibility. In other words, any ordered pair (bushes,trees) with integer coordinates that lies within the area (including on the boundaries) is a possible combination that Linda could purchase from her supplier. Note that we had to put the 'integer coordinates' restriction in there because it is highly unlikely that a supplier will sell a fractional part of either a bush or a tree.