First, we need to convert the child's weight from pounds to kilograms. One pound is  equal to 0.4536 kilograms, so 88 pounds is equal to 0.4536 x 88 = 39.9168 kilograms.  Next, we need to find the maximum safe dose of amoxicillin for this child based on the  recommended dosage of 50 mg/kg/24 hour. To do this, we multiply the child's weight by  50 mg/kg, which gives us 39.9168 x 50 = 1995.84 mg/24 hour.  

This means that the child should not receive more than 1995.84 mg of amoxicillin in a  day.  

Then, we need to find the amount of amoxicillin in each dose based on the prescribed  frequency of every 8 hours. To do this, we divide the maximum safe dose by the number  of doses in a day, which is 24 hours divided by 8 hours, or 3 doses. This gives us 1995.84  / 3 = 665.28 mg/dose.  

This means that each dose of amoxicillin should not exceed 665.28 mg. 

Finally, we need to find the volume of the suspension that contains this amount of  amoxicillin based on the label information of Amoxicillin Suspension 250 mg/5 mL. To do  this, we use a proportion:  

250 mg / 5 mL = 665.28 mg / x mL 

Cross-multiplying and solving for x, we get: 

x = (665.28 x 5) / 250 

x = 13.3056 mL 

Therefore, the nurse should administer 13 mL of the suspension for each dose.