Posted by piinkkk! on Thursday, November 5, 2009 at 12:28pm.
Mr. Green, the Herbarium's owner, has come to you with another problem to solve. He wants to create a new sales display featuring giant potted plants and plants in smaller hanging baskets. He wants to set up the display in such a way that he can maximize his profit from that area, but doesn't know how many of each plant type to use. He provides you with certain parameters that limit the number of potted plants and hanging baskets he can use in the display. Use the following information to tell Mr. Green how many giant potted plants and how many plants in hanging baskets he should display to maximize his profits.
Mr. Green wants to dedicate no more than 168 square feet to the display. Each giant potted plant requires 7 square feet of space. Each hanging basket requires 4 square feet of space. The Herbarium has 210 gallons of soil available to pot the plants for the display. Giant potted plants need 14 gallons of soil each while the hanging baskets need 2 gallons of soil each. Mr. Green has allocated $252 to buy the plants for this display. Giant potted plants cost $14 each while the plants for hanging baskets cost $5 each. The Herbarium makes a profit of $28 on each giant potted plant sold, and a profit of $8 on each plant in a hanging basket sold.
A. Declare a set of variables pertaining to Mr. Green's situation and write a system of inequalities that models Mr. Green's situation. There are directions for how to type math characters in the Resource Center that will show you show to enter your inequalities
p= giant potted plants h= hanging baskets
x= p y= h
7p + 4h <= 168 sq. ft.
7x + 4y <= 168
14p + 2h <= 210gallons of available soil.
14x + 2y <= 210
$14p + $5h <= $252
$14x + $5y <= $252
P= 28p + 8h
B. Describe the solution graph by giving the boundaries of the solution area as inequalities and state the relationship of the solution to the inequality, i.e.: above, below, to the left, to the right, etc.
 ?!?!?!? help?

algebra 2.  MathMate, Thursday, November 5, 2009 at 10:53pm
Part A:
The inequalities of part A are correct.
Missed out are the conditions
x≥0 and y≥0.
The objective function P=28P+8H is doubtful, because there is no statement saying that sales are proportional to the number of samples on display.
Part B:
You will have to plot the graphs and find out what the lines look like. Since all your inequalities are ≤, so the feasible regions are all below the lines plotted. In fact, the final feasible region will be the polygon below all the lines plotted, and above the xaxis, and to the right of the yaxis.
You will find four vertices at the top of the feasible region, places where solutions are most likely to lie.
You will evaluate the objective function at these four vertices and choose the most favourable one.
As a check, these vertices are associated with values of x of 0,8,13 and 15.
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