Math

P=20x+30y

subject to:
2x+3y>30
2x+y<26
-6x+5y<50
x,y >0

1. Two ways:
Graphical...
plot the contraint areas 2x+3y=30
2x+y=26
-6x+5y=50
x,y >0
Now we have a nice theorem that states the max, and min, will occur on the boundry where constraint lines meet. So test the profit function 20x+30y at each corner, and you will find the max.

Second method: Analytical
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=1e692c6f72587b2cbd3e7be018fd8960&title=Linear%20Programming%20Calculator&theme=blue

posted by bobpursley
2. looks like linear programming.

let's look at each region.
2x + 3y > 30
the boundary is 2x + 3y = 30
when x = 0, y = 10
when y = 0 , x = 15 , so we have (0,10) and (15,0)
plot these points on the axes and draw a dotted line,
shade in the region above this line

2x+y < 26
repeat my method, shade in the region below the line 2x+y = 26

careful with the last one, I will do that one as well.
-6x+y < 50 -----> y < 6x+50
draw the boundary line y = 6x+50
when x=0, y = 50 , when y = 0 x = -25/3
so your two points are (0,50) , (-25/3,0)
shade in the region below that line

Your boundary lines should look like this
http://www.wolframalpha.com/input/?i=plot+2x+%2B+3y+%3D+30,+2x%2By+%3D+26,+y+%3D+6x%2B50

and here the actual intersection of the shaded regions.
http://www.wolframalpha.com/input/?i=plot+2x+%2B+3y%3E+30,+2x%2By+%3C+26,+y+%3C+6x%2B50

notice that P = 20x + 30y has the same slope as 2x + 3y = 30
so the farthest point to the right of your region will be the solution.
Solve the corresponding equations to find that point, plug into
P = 20x + 30y

posted by Reiny

Similar Questions

1. Math

why is this not correct 30y = x^2 - 14x + 13 - 13 30y - 13 = x^2 - 14x _________ ___________ -14 -14 x = sqrt 30y-13 _______ -14 sorry the division signs didn't line up
2. MATH ALGEBRA

Which of the following coordinates are intercepts of the linear relation 2x- 3y + 30 = 0 ? I. (0 , 10) II.(0 , 2/3) III.(-10 , 0) IV.(-15, 0) A. I only B. I and IV only C. II and III only D. II and IV only This was what I was

5 - sqrt of 20x + 4 >= -3 5- 20x + 4 >= -3 5-4 - 20x >= -3 1 - 20x >= -3-1 -20x >= -4 x<= -15 Possible answers are x<=3 -1/5 <= x<= 3 x >= -1/5 x >= 0 I think it is -1/5<=x<=3 because both
4. Math

Maximize P = 16x + 80y subject to these constraints: 2x + 20y ≤ 430 4x + 70y ≤ 1400 8x + 30y ≤ 980 10x + 10y ≤ 1000 4x + 30y ≤ 700 x ≥ 0, y ≥ 0 Maximum value for P = ?. This value of P
5. Linear Programming

Maximize P = 16x + 80y subject to these constraints: 2x + 20y ≤ 430 4x + 70y ≤ 1400 8x + 30y ≤ 980 10x + 10y ≤ 1000 4x + 30y ≤ 700 x ≥ 0, y ≥ 0 Maximum value for P = ?. This value of P
6. Math Help

What is the sum or difference? A)-7y^5* B)-30y^5 C)-30y^10 D)-7y^10
7. math

5(3+4x)-6>=129 I get 2 different answers on this one. 15+20x-6>=129 15+20x-6+6>=129+6 15+20x>=135 15-15+20x>=135-15 20x>=120 20x/20>=120/20 x>=6 Is this worked out properly, are there any shortcuts?
8. Math

Find the intersection of two lines. i have the answer just please tell me how it was made 4x-3y-4=0 , 4x+2y+5=0 -5y/-5 = 9/-5 y= 9/5 4x-3(-9/5)-4=0 5(4x+27/5-4=0) 20x+27-20=0 20x+7=0 20x/20=-7/20 x=-7/20 (-7/20, -9/5
9. algebra

20. At a local candy store, Malcolm purchased some 25-cent candies and some 30-cent candies. He spent a total of \$4.75. Which equation below describes the number of each type of candy he bought? A25x + 30y = 4.75 Bx + y =
10. algebra

How do you simplify (4x^3y^5)^2? are you using the carrots for symbolising "the power of..." or fractions? if i know what your using them for then i can help you. yes. 3^2=9 okay. then it would help to put the exponents out of the

More Similar Questions