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 \\( \\$ 5.70 \\) per day. After analyzing its costs, Hardyke calculates that, with its operating deficit, the full cost of each student for a day is \\( \\$ 8.20 \\). 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 3,700 student-days for in-need children in a given month, what is the monthly value of the difference between the prices in full capacity