They must produce 100 units to achieve the lowest average cost.
As we know that to achieve lowest average cost the average cost function and marginal cost function must be equal.
That is , MC=ATC
⇒ [tex]2Q^{2} + 50Q = Q^{2} + 50Q + 10000\\[/tex][tex]Q^{2}[/tex]
⇒ [tex]Q^{2} = 10000[/tex]
⇒ Q = 100
So , 100 units must be produced to achive lowest average cost.
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