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 $$1$ per day, to be paid by the student. The government will reimburse Hardyke for the "cost" of providing daily services used by a student. The regular price to participate in the program is $$5\mathrm{.}90$ per day. After analyzing its costs, Hardyke calculates that, with its operating deficit, the full cost of each student for a day is $$8\mathrm{.}40.$ 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 $3,900$ student$-$days for in$-$need children in a given month, what is the monthly value of the difference between the prices in full capacity?