A store sells $Q$ units of a product per year. It costs $d$ dollars to store one unit for a year. To reorder, there is a fixed cost of $b$ dollars, plus $c$ dollars for each unit. How many times per year should the store reorder, and in what lot size, in order to minimize inventory costs? Use the general solution to find how many times per year a store should reorder, and in what lot size, when $Q=100$, $d=\$ 20, b=\$ 40$, and $c=\$ 15$.
\[
\begin{array}{l}
\text { order size }=\sqrt{\frac{Q d}{2 b}} \\
\text { lot size }=\sqrt{\frac{2 b Q}{d}}
\end{array}
\]

Step 1 ：We are given that the store sells \(Q = 100\) units of a product per year. It costs \(d = \$20\) to store one unit for a year. To reorder, there is a fixed cost of \(b = \$40\) dollars, plus \(c = \$15\) dollars for each unit.

Step 2 ：We are asked to find how many times per year the store should reorder, and in what lot size, in order to minimize inventory costs.

Step 3 ：The general solution to this problem is given by the formulas for order size and lot size: \[\text{order size} = \sqrt{\frac{Qd}{2b}}\] and \[\text{lot size} = \sqrt{\frac{2bQ}{d}}\]

Step 4 ：Substituting the given values into these formulas, we find that the order size is \(5.0\) and the lot size is \(20.0\).

Step 5 ：Thus, the store should reorder \(\boxed{5}\) times per year and the lot size should be \(\boxed{20}\) units.