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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 $A$.

Albert
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Raunak Bag
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1 Answers1

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I suppose that, implicitly, $x$ is the quantity of doll $A$ which is produced, and $y$ is the quantity of doll $B$ which is produced (on a given day). Suppose that one of each doll type is made. Then, in terms of time units it takes to make doll $A$, you have one time unit from the one doll $A$ produced and two time units from the one doll $B$ that is produced -- that is, it takes $x + 2y$ time units (with $x = 1$ and $y = 1$ in our example). Does this make sense?

Tom
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  • okay..that part is clarified..but now can't relate with "The company have time to make a maximum of 2000 dolls of type A per day" – Raunak Bag Dec 31 '15 at 20:47