Can someone help me with this problem in linear programming ?

6. Jon and his two cats Jupiter and Zeus are trying to figure out how to spend up to 12 hours of their daily routine. Their daily routine can include the activities included below in the table results in a specific amount of happiness or sadness (negative happiness) for each of the three creatures. If they are idle they receive no (0) happiness. Activity Motorcycling Cleaning Making a Mess Jon 5 -3 Jupiter 2 Zeus 4 Petting Getting Petted 1.5 3 2 IEOR 162 Homework 12 Linear Programming & Network Flows - Page 2 of 5 Out: April 14, 2022 Due: April 22, 2022 The happiness score for each creature is determined by the score given in the table multiplied by the amount of time spent on the activity. For instance if Jon spends his day cleaning for half an hour and motorcycling for an hour then his happiness score would be 5(1)+(-3)(0.5) = 3.5. There are some natural restrictions on how they can allocate their time. Specifically For every hour Jupiter or Zeus spend 'Making a Mess' Jon must spend half an hour (0.5 hours) 'Cleaning'. Jon must spend the same amount of time 'Petting' as Jupiter and Zeus spend 'Getting Petted' added together. For fairness purposes, Jon, Jupiter, and Zeus have decided to allocate their time such that the lowest happiness score among the three of them is as large as possible. Specifically, the least of the three happiness scores resulting among Jon, Jupiter, or Zeus should be maximized. Formulate a Linear Program that will help Jon, Jupiter, and Zeus figure out how to spend their a time optimally such as to maximize the minimum happiness score. 6. Jon and his two cats Jupiter and Zeus are trying to figure out how to spend up to 12 hours of their daily routine. Their daily routine can include the activities included below in the table results in a specific amount of happiness or sadness (negative happiness) for each of the three creatures. If they are idle they receive no (0) happiness. Activity Motorcycling Cleaning Making a Mess Jon 5 -3 Jupiter 2 Zeus 4 Petting Getting Petted 1.5 3 2 IEOR 162 Homework 12 Linear Programming & Network Flows - Page 2 of 5 Out: April 14, 2022 Due: April 22, 2022 The happiness score for each creature is determined by the score given in the table multiplied by the amount of time spent on the activity. For instance if Jon spends his day cleaning for half an hour and motorcycling for an hour then his happiness score would be 5(1)+(-3)(0.5) = 3.5. There are some natural restrictions on how they can allocate their time. Specifically For every hour Jupiter or Zeus spend 'Making a Mess' Jon must spend half an hour (0.5 hours) 'Cleaning'. Jon must spend the same amount of time 'Petting' as Jupiter and Zeus spend 'Getting Petted' added together. For fairness purposes, Jon, Jupiter, and Zeus have decided to allocate their time such that the lowest happiness score among the three of them is as large as possible. Specifically, the least of the three happiness scores resulting among Jon, Jupiter, or Zeus should be maximized. Formulate a Linear Program that will help Jon, Jupiter, and Zeus figure out how to spend their a time optimally such as to maximize the minimum happiness score