I learned in economics that the main reason why Aggreggate planned expenditure (APE) and real GDP are not always equal is because of inventories. This is entirely understandable. However, HOW they are related is a bit confusing. If APE exceeds real GDP, then they sell more than they produce. This confuses me. If they sell more than they expect, wouldn't real GDP exceed their APE?

If aggregate planned expenditure exceeds real GDP, then

What are the objectives of macroeconomis?

I am not 100% sure if I am correct but real GDP is the measure of what is produced in a country, so when real GDP exceeds pAE, what firms produced was more than they had planned. Now with the eqn GDP = C + I + G + X - M, and C G X M are fixed, ceteris paribas, it would mean the firms have to increase their investment in their inventory. Think of pAE vs real GDP as firms were thinking of producing this amount but they ended up producing more. If you read it backwards it makes more sense. Since real GDP exceeds pAE, it means that firms produced more than they had planned to, hence this production is an investment in their inventory.