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Balance = 1,360 USD

Cost = (0.0001% * Purchase Qty * Purchase Qty) + (1% * Purchase Qty)

Problem: Find maximum Purchase Qty while keeping Cost below Balance.

Is there a closed form solution to this?

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  • $\begingroup$ The equation is $10^{-6}\cdot q^2+10^{-4}\cdot q=1360 $. Comprehensible? $\endgroup$ Commented Mar 23, 2023 at 18:50

1 Answer 1

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Let the quantity be $q$. $$1360=10^{-6} \cdot q^2$$ $$q^2=1.36 \cdot 10^9$$ $$q = \sqrt{1.36 \cdot 10^9} \approx 3.688 \cdot 10^4$$

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