At a certain factory, the total cost of manufacturing q units during the daily production run is $C ( q ) = 0.3 q ^ { 2 } + 0.8 q + 800$ dollars. It has been determined that approximately $q ( t ) = t ^ { 2 } + 80 t$ units are manufactured during the first t hours of a production run. Compute the rate at which the total manufacturing cost is changing with respect to time 2 hours after production begins.

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The Answer of At a certain factory, the total cost of manufacturing q units during the daily production run is $C ( q ) = 0.3 q ^ { 2 } + 0.8 q + 800$ dollars. It has been determined that approximately $q ( t ) = t ^ { 2 } + 80 t$ units are manufactured during the first t hours of a production run. Compute the rate at which the total manufacturing cost is changing with respect to time 2 hours after production begins.

At a Certain Factory, the Total Cost of Manufacturing Q C(q)=0.3q2+0.8q+800C ( q ) = 0.3 q ^ { 2 } + 0.8 q + 800C(q)=0.3q2+0.8q+800

At a Certain Factory, the Total Cost of Manufacturing Q $C ( q ) = 0.3 q ^ { 2 } + 0.8 q + 800$