Hardyke Group operates a local after$-$school recreation and activities program. The Education Department is a state governmental

agency. Hardyke has an agreement with the Department to provide services to students in need for a nominal $$1$ per day, to be paid

by the student. The government will reimburse Hardyke for the "cost" of providing daily services used by a student.

The regular price to participate in the program is $$6\mathrm{.}80$ per day. After analyzing its costs, Hardyke calculates that, with its operating

deficit, the full cost of each student for a day is $$9\mathrm{.}30.$ All programs that Hardyke offers are unaffected by the number of students

paying the nominal fee.

Required:

b$.$ Which price would Hardyke Group prefer?

Note: Enter your answer to $2$ decimal places.

c$.$ Which price would the Education Department prefer?

Note: Enter your answer to $2$ decimal places. Leave no cells blank $-$ be certain to enter $"0"$ wherever required.

d$.$ If Hardyke provides an average of $4,800$ student$-$days for in$-$need children in a given month, what is the monthly value of the

difference between the prices in full capacity?