I am having trouble with the following problem:
A manufacturer of hospital supplies has a uniform annual demand for $180, 000$ boxes of bandages. It costs $20$ dollars to store one box of bandages for one year and $320$ dollars to set up production. How many times a year should the manager decide to produce boxes of bandages in order to minimize the total cost of storage and setup?
I think this problem is a little bit unclear. If it costs $20$ dollars to store one box for a year, I'm not sure that this implies a one time flat fee of $20$ dollars, or if it means that storing it for half a year will only cost $10$ . I can see the tradeoff between making too many or too few bandages in one run, but I can't quite put it into equations.
Best Answer
This exercise can be managed by using the EOQ-formula.
In your case the total costs are
$TC=\frac{K \cdot D}{Q}+\frac{Q\cdot h}{2}=\frac{320 \cdot 180,000}{Q}+\frac{Q\cdot 20}{2}$
$P$ = store costs per year
$Q$ = produce quantity
$D$ = annual demand quantity
$K$ = Set up production cost
$h$=storage cost per unit
The derivative w.r.t Q is
$\frac{\partial TC}{\partial Q}=-\frac{K \cdot D}{Q^2}+\frac{ h}{2}=0$
Solving for Q
$\frac{K \cdot D\cdot 2}{h}=Q^2$
$Q^*=\sqrt{\frac{K \cdot D\cdot 2}{h}}$
After you have calculated the optimal produce quantity the number of cost minimizing set ups is $\frac{D}{Q^*}$