Originally posted by: oboeguy
OP's friend is incredibly clueless if he can't understand that 1) addition commutes and 2) the profit function could have been written the terms in a different order in the first place!
You missed the most fundmental point #3. The profit equation can be rewritten as:
(Profit) = (Direct profit per unit) * (number of units) - (Fixed costs).
Direct profit per unit is defined as revenue per unit minus variable direct costs per unit.
P = (50-20) * x - 8000
In fact, the poriton (50-20) = 30 is probably THE most important part of the entire lesson. Not only can they be combined, they SHOULD be combined. Why? In many business decisions, the fixed costs should not be considered. For example, if you are stuck in a lease for 5 years at $10000/month yet you can sell your goods at a direct profit of $9000, should you close shop even if you are losing money? No. Because staying in businees loses you $1000/month, but closing up costs you $10000/month. The reason to stay in business is that the direct profit is positive.