Question

Previous Problem List Next (1 point) In a certain factory, the cost to produce q items during a single production run is estimated to be C(q) = 50q+0.005q² + 1000 (dollars). The factory utilizes 12-hour production runs and it is estimated that the number of units that can be produced in the first t hours of a production run is given by: 300+ if 0 <t<4 g(t) = 260t + 160 if 4 < t < 8 292t - 2+2 + 32 if 8<t< 12 If the answer to one of the questions below is Does Not Exist, just enter DNE. A) How fast is the production run cost changing with respect to time at 2 hours? 1106 (dollars/hour). B) How fast is the production run cost changing with respect to time at 4 hours? 62 (dollars/hour) C) How fast is the production run cost changing with respect to time at 8 hours? 260 (dollars/hour) D) The AVERAGE cost per item to produce the first q items is C(2). How fast is the average cost per item changing with respect to time at 10 hours? 9 Idollars./item/hour

Answer 1

C(q) = 509 + 0.005q2 + 1000 dc aq so + 0.005(29) +00 A) t=2 9(2): 300(2) = 600 dq 300 de dc at de da aq et (50+ 0.01600) 300 56 X 300 16800 dollars/hour. 0.01 X1200 q(4) - 300x4 = 1200 de (so + 01 X1200](300) to 62x300 118600 dollars/hour. -

c ) 2(8) - २८0x8 +160 %3D 2080 +160 २२५० 260 - dc. क (504 0.01 x 22५०)(260) (72.५)(260) 2 2 ।। 8824 C(a) 50 + 0.0059 + 1000 2 १ dc). delde D.DOS + - 1000 व 22 940)- 99210) - २10) +32 = 2752 Idag वह (ब) (0.005 10.005+ -1000 292 - २(2X10) (9754) 11. 226726 doller/iten / now.

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