question archive The Egghead Smartphone Company receives 630 cases of imported memory cards every 18 days
The Egghead Smartphone Company receives 630 cases of imported memory cards every 18 days
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The Egghead Smartphone Company receives 630 cases of imported memory cards every 18 days. The number of cases of memory cards on inventory t days after the shipment arrives is N(t)=630−35(root18t). Find the average daily inventory.
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Egghead Smartphone Company receives 630 cases of imported memory cards every 18 days
N(t)=630−35(√18t)
formula which we are using
average daily inventory = (1/T) ∫0TN(t) dt
= (1/18) ∫018 630−35(√18t) dt
= (1/18) ∫018 (630) − 35(√18t) dt
= (1/18) ∫018 (630) − 35√18√t) dt
= (1/18) [ 630t − 35 *√18 *(t3/2/(2/3) ) ]018
= (1/18) [ 630t − 35 *√18 *(2/3)t2/3 ]018
= (1/18) [ 630t − (70√18/3)t3/2 ]018
= (1/18) [ 630(18-0) − (70√18/3)(18-0)3/2 ]
= (1/18) [ 11340 − (70√18/3)(183/2 ]
= (1/18) [ 11340 − (70/3) √18 *(18)3/2 ]
= (1/18) [ 11340 − (70/3) (18)2 ]
= (1/18) [ 11340 − (7560) ]
= (1/18) *(3780) = 210
average daily inventory = 210 is answer
