Optimization with Constraints

Question

I went to a shop to purchase some refills costing Rs. $1.60$ each but the clerk did not have change for my $20$-rupee note. I was constrained to purchase some $30$ paise labels as well so that no money needed to be returned. After purchasing the maximum number of refills under the given constraints, how many labels did I have to purchase?

Accepted Answer

D. Let $r$ be the number of refills and $l$ be the number of labels. $$160r + 30l = 2000$$ Dividing by 10: $16r + 3l = 200$. We want to maximize $r$. The maximum possible value for $r \le \lfloor 200/16 \rfloor = 12$. - If $r = 12$: $16(12) = 192$, remaining $= 8$, which is not divisible by 3. - If $r = 11$: $16(11) = 176$, remaining $= 24$, which is divisible by 3 ($24 / 3 = 8$). Thus, $r = 11$ and $l = 8$.

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2

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4

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6

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8

Optimization with Constraints

Explanation

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