Algebra 2: using linear programming to maximize profits

(onfus3d

New member
Joined
Nov 21, 2006
Messages
3
A concession stand makes $0.85 on each regular hot dog and $1.30 on each foot-long hot dog. On a typical Saturday, the stand sells between 25 and 40 regular hot dogs and between 30 and 50 foot-longs. The total sales have never exceeded 80 hot dogs. How many of each type should be prepared to maximize profit?

so for this problem you have to make a system of inequalities and they are:

r>=0
f>=0
25<=r<=40
30<=f<=50
r+f<=80

then you have to graph the inequalities but after that what do you do?
 
does any body know what i should do next?? i really need help.. i dont' know what to do... making the graph is as far as i've gotten
 
Why not just graph what you have?

Profit = 0.85*r + 1.3*f

f = (Profit - 0.85*r)/1.3

Hit all the corners.

(25,50) ==> Profit = 86.25
(40,30) ==> Profit = 73.00
(40,40) ==> Profit = 86.00
(30,50) ==> Profit = 90.50

 
Top