The cost C (x) in dollars per day to operate a delivery service is given by C (x) = cubed root of x (all of that) + 800, where x is the number of deliveries per day. If it is necessary to keep costs below $1885, what is the greatest number of deliveries that can be made to achieve this goal?

Given that C (x) = x³+800, where x is the number of deliveries per day. If it is necessary to keep cost below $1885, the greatest number of deliveries that can be made to achieve this goal will be found as follows:

for cost to remain at $1885 we shall have:

1885=x³+800

solving for x we shall have:

1885-800=x³

1085=x³

getting the cube root of both sides we shall have:

∛1085 = (∛x³)

x=10.276

thus the number of trips should be at most 10 trips