Delilah is studying for her exams in Astrobiology and Cryptozoology. However given her time commitments, she...

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Delilah is studying for her exams in Astrobiology and Cryptozoology. However given her time commitments, she only has one 4 hour block (240 minutes) of spare time available each day to study. She plans to split each 240 minute block into a number of 45 minute sessions for Astrobiology and a number of 30 minute sessions for Cryptozoology. To successfully pass her exams, she estimates she needs at least 28 (45 minute) study sessions for Astrobiology and at least 84 (30 minute) study sessions for Cryptozoology. The only restriction is that she wants to study at least one (45 minute) Astrobiology session and at least one (30 minute) Cryptozoology session in each 4 hour (240 minute) block. Delilah notes that some of the 240 minute study block will not be used completely depending upon how many sessions for each course is studied. For instance, if she decides to divide the 240 minute block into three sessions for Astrobiology (45minutes) and three sessions for Cryptozoology (30 minutes) then this would leave 15 minutes of the 4 hour block for that day which is not used (240-3 x 45-3 x 30 = 15). She also wants to minimise the total number of days (i.e. number of 4 hour study blocks) to be used for study. Help Delilah with this study problem using linear programming. Provide a practical answer. Delilah is studying for her exams in Astrobiology and Cryptozoology. However given her time commitments, she only has one 4 hour block (240 minutes) of spare time available each day to study. She plans to split each 240 minute block into a number of 45 minute sessions for Astrobiology and a number of 30 minute sessions for Cryptozoology. To successfully pass her exams, she estimates she needs at least 28 (45 minute) study sessions for Astrobiology and at least 84 (30 minute) study sessions for Cryptozoology. The only restriction is that she wants to study at least one (45 minute) Astrobiology session and at least one (30 minute) Cryptozoology session in each 4 hour (240 minute) block. Delilah notes that some of the 240 minute study block will not be used completely depending upon how many sessions for each course is studied. For instance, if she decides to divide the 240 minute block into three sessions for Astrobiology (45minutes) and three sessions for Cryptozoology (30 minutes) then this would leave 15 minutes of the 4 hour block for that day which is not used (240-3 x 45-3 x 30 = 15). She also wants to minimise the total number of days (i.e. number of 4 hour study blocks) to be used for study. Help Delilah with this study problem using linear programming. Provide a practical answer.

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