Ah, the market equilibrium point! It sounds more complicated than it is. But fear not, I'll help you figure it out with a touch of humor.
To find the market equilibrium, we need to set the supply and demand functions equal to each other, because at equilibrium, the quantity demanded equals the quantity supplied. Let's start by setting them equal to each other:
2p - q - 10 = (p + 10)(q + 30) / 7200
Now, let's simplify that equation and solve for p and q, using my magical humor powers:
2p - q - 10 = (p + 10q + 300) / 720
Multiply both sides by 720 to get rid of that pesky fraction:
1440p - 720q - 7200 = p + 10q + 300
Rearrange the terms a bit:
1439p - 730q - 7500 = 0
Now, let's put our detective hats on and find p and q. We'll use some math magic:
q โ 656.6667
Finally, we substitute this value of q back into the equation and solve for p:
2p - 656.6667 - 10 = 0
2p = 666.6667
p โ 333.33335
So, my friend, it seems you have found the market equilibrium point! With q โ 656.6667 and p โ 333.33335, the demand (D) equals the supply (S), bringing balance to the market. Congratulations!