i have a total of 1000 rs. item A costs 110 rs. , B costs 90 rs. , C costs 70 rs. , D costs 40 rs. , and E costs 45 rs. for every item D that i purchase, i must also buy two items of B. For every item A , i must buy one of item C. for every item E, i must also buy two of item D and one of item B. For every item i purchase i earn 1000 points and for everry rs. not spent i earn a penalty of 1500 points. my objective is to maximise the points i earn. how many items must i purchase to maximise my points?

To maximize the points earned, we have to maximize the number of items bought and minimize the number of points lost.
We can maximize the number of items bought by buying the item of the least cost, i.e., C, which is Rs 70.
If we buy 14 items of C, we are left with Rs 20, which will give a loss of 30000 points. Instead, if we buy 13 items of C and 1 item of B, then we spent all Rs 1000 and bought the highest number of items possible. So, we have to buy 14 items.

But we can further maximise the profit by the following consideration. As we know from the question that: for every item E we buy, we need to buy 2 items D and 1item of B, which makes the total cost as Rs 215 and the total items bought as 4 in this particular purchase . Now, if we buy 4 of item E along with the aforementioned items , we will spend Rs 860 and will get 16 items in return.Now, for the full expenditure of Rs 1000, if we further buy 2 items of C for Rs 140, all the money would be spent and we will get the maximum profit of 18000 points. So, why cant we solve this question by this method? If anybody can help then please do!!!

This is my response to Surbhi's query. Were you to buy 1 E you'd have to buy 2D and 1B. Now for each D, you'd have to buy 1 B. So let's say if you buy 4 Es you'll not be having 8D and 4B but 8D and 12B which can't be bought with 1000.

Thanks for help

Answer should be 13.

But this violated the condition for 1A there is 1C