# [SOLVED] Use graphical methods to solve a linear programming problem

• Jan 18th 2010, 08:43 PM
majax79
[SOLVED] Use graphical methods to solve a linear programming problem
NVM
• Jan 18th 2010, 11:52 PM
earboth
Quote:

Originally Posted by majax79
A math camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is$1100. The camp can accomodate up
to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize
cost?

a. Define variables.
b. Write a system of linear inequalities to model this problem.

To a):

s := monthly salary
c := number of counselors
a := number of aides

to b):

$\displaystyle \left|\begin{array}{l}a+c \ge 30 \\ a+c \le 45 \\ a \ge 10 \\ 2c \le 3a\end{array} \right.$ Solve these inequalities vor c and draw the graphs. Determine the feasible polygon. Use the vertex which produces the lowest parallel to the line describing the salary.

and:

$\displaystyle s = 2400 \cdot c + 1100 \cdot a$

I've got 30 aides and 0 counselors would cause the lowest costs.
• Jan 18th 2010, 11:54 PM
earboth
Quote:

Originally Posted by majax79
Anyone?

I'm just curious: What have you done during the last 3 hours? (beside typing "Anyone?")
• Jan 19th 2010, 12:00 AM
majax79
I've been working on this problem...oh and I masturbated too.
• Jan 19th 2010, 12:01 AM
pickslides
Quote:

Originally Posted by majax79
oh and I masturbated too.

(Rock)