Is this Minimization problem set up correctly?

Here's the question:


A restaurant wants to hire cooks and waiters at a minimum wage cost. The average monthly salary of a cook is $2000 and the average monthly salary of a waiter is $800. The restaurant can accomodate up to 25 staff and needs at least 20 to run properly. They must have at least 9 waiters, and may have up to 6 waiters for every 4 cooks. How many cooks and how many waiters should the camp hire to minimize cost?





Here's my equation to set it up:


c = # of cooks


w = # of waiters


c+w =%26lt; 25


c+w =%26gt; 20


w =%26gt; 9


6w =%26lt; 4c


Cost = C = 2000c + 800w


Then I did the Minimization Simplex method and placed all of these formulas in the simplex tableau, but I keep going around in circles and receiving negatives at the bottom of the tableau. What have I done wrong?

Is this Minimization problem set up correctly?
Your equation for "up to 6 waiters for every 4 cooks" is wrong. It should be 4w ≤ 6c (from w≤ 6(c/4)), or 6c - 4w ≥ 0