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I have a total of Rs. 1,000. Item A costs Rs. 110, item B costs Rs. 90, item C costs Rs. 70, item D costs Rs. 40 and item E costs Rs. 45. For every item D that I purchase, I must also buy two of item 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 purchased I earn 1000 points and for every rupee not spent I earn a penalty of 1500 points. My objective is to maximise the points I earn. What is the number of items that I must purchase to maximise my points?

1. 13
2. 14
3. 15
4. 16

+1 vote

there are 3 sets

(1) For every item A, I must buy one of item C

so (A,C) in one set and total costs of (A,C) is 110+70=180

(2) Similarly (D,2B) in another set , total costs is 40+180=220

(3) Similarly (E,2D,B) in another set , total costs is 45+80+90=215

Now, to maximize my point , I  have to maximize my perchase , so small amount left in my hand

Now, if we take set (3) two times we get a perchase of Rs.430

Again if we take set (1) 3 times total cost will be Rs. 540

Total spend  430 + 540 =970 Rs.

That is most close range for total Rs.1000

So, total no of items 4*2 + 2*3 =14