Hi, there. I'm happy to help with this.
Let's call the selling price, the retail price, P.
The producer allows the sales person to take a 36% commission, so the sales person pockets 0.36*P. That means, the producer gets 0.64*P.
Now, we are told, this 0.64*P that the producer pockets represent a 8.8% profit. In other words, if the producer's cost is C, he is now pocketing 1.088*C.
1.088*C = 0.64*P ------ divide both sides by 0.64
1.7*C = P
That equation relates the cost and the price. Assume neither of those changes.
In the second half of the problem, the wording is
atrociously ambiguous --- does the commission drop 24 percentage points to a 12% commission, or does it decrease by 24% to 36%*(0.76) = 27.36%??? The real GMAT will not give you a problem with such a screaming ambiguity in its wording. For simplicity, I am going to assume they mean: the commission dropped 24 points to an even 12% commission.
Now, the poor salesperson pockets only 0.12*P (and, with income reduce to 1/3 of its previous value, presumably has trouble paying rent). The producer, meanwhile, pockets 0.88*P. In terms of cost, this is:
0.88*P = 0.88*(1.7*C) = 1.496*C
That's a 49.6% profit over and above cost, so that's the new profit for the producer.
Does all that make sense?
Please let me know if you have any questions.
Mike
