Here is the given question: A toy manufacturer produces two types of dolls; a basic version doll $A$ and a deluxe version doll $B$. Each doll of type $B$ takes twice as long to produce as one doll of type $A$. The company have time to make a maximum of $2000$ dolls of type $A$ per day, the supply of plastic is sufficient to produce $1500$ dolls per day and each type requires equal amount of it. The deluxe version, i.e type $B$ requires a fancy dress of which there are only $600$ available per day. If the company makes a profit of $₹ 3$ and $₹ 5$ per doll, respectively, on doll $A$ and doll $B$; how many of type should be produced per day in order to maximize the profit?
Now, in the solution the equation involving the time required and available is given as: $x + 2y ≤ 2000$ (where $x$ dolls of type $A$ and $y$ dolls of type $B$ are produced per day to maximize the profit.) But shouldn't the equation be $2x + y ≤ 2000$ OR $x + (1/2)y ≤ 2000$ ? Please explain how to interpret the problem correctly. In my logic, since type B dolls takes twice the time to produce compared to doll $A$, only half of them could be produced in a given time as compared to $A$.