update R7 R7X R8a

reviews/R8a.md

@@ -0,0 +1,58 @@
+# Review 7
+
+* Hajin Ju, 2024062806
+
+## Problem 1
+
+Fill in the blanks in the following assembly-line scheduling example.
+
+### Solution 1
+
+![](/assets/R8-1_1.png)
+
+
+**table $s$**
+
+| $s$ | 1   | 2   | 3   | 4   | 5   | 6   |
+| --- | --- | --- | --- | --- | --- | --- |
+| 1   | 9   | 18  | 20  | 24  | 32  | 35  |
+| 2   | 12  | 16  | 22  | 25  | 30  | 37  |
+
+**table $l$**
+
+| $l$ | 1   | 2   | 3   | 4   | 5   | 6   |
+| --- | --- | --- | --- | --- | --- | --- |
+| 1   | -   | 1   | 2   | 1   | 1   | 2   |
+| 2   | -   | 1   | 2   | 1   | 2   | 2   |
+
+$$\begin{align*}s^* &= 38\\l^* &= 1\end{align*}$$
+
+## Problem 2
+
+Fill in the blanks in the following pseudocode for assembly-line scheduling
+
+### Solution 2
+
+```python
+FASTEST-WAY(a, t, e, x, n)
+    s[1][1] = e[1] + a[1][1]
+    s[2][1] = e[2] + a[2][1]
+    for j = 2 to n
+        do
+        if s[1][j-1] + a[1][j] <= s[2][j-1] + t[2][j-1] + a[1][j]
+            then s[1][j] = s[1][j-1] + a[1][j]
+                l[1][j] = 1
+            else s[1][j] = s[2][j-1] + t[2][j-1] + a[1][j]
+                l[1][j] = 2
+        
+        if s[2][j-1] <= s[1][j-1] + t[1][j-1]
+            then s[2][j] = s[2][j-1] + a[2][j]
+                l[2][j] = 2
+            else s[2][j] = s[1][j-1] + t[1][j-1] + a[2][j]
+                l[2][j] = 1
+    if s[1][n] + x[1] <= s[2][n] + x[2]
+        then s* = s[1][n] + x[1]
+            l* = 1
+        else s* = s[2][n] + x[2]
+            l* = 2
+```