Constrained Optimization problem, need help with all of these questions please! if you cant do all of them just do the ones you can, thank you!

1. Thom is a singer-songwriter from Oxford, England who is in some band. Thom likes two things: appealing to the public, and satisfying his own creative endeavors. Therefore, every song. Thom writes has public elements (p), and creative elements (c). In fact, Thom thinks he can measure his happiness by using the utility function U(p,c)=3p2c11. However, Thom's label says he only has 236 seconds of time to make the best song he can. Each second in the song can be either "for the public" ( p ) or "for Thom" (c). How should Thom construct his debut single "Creep" in terms of the optimal bundle of public elements and creative elements? 2. "Creep" is released on September 21st, 1992 and it peaks at number 34 on the Billboard Hot 100 in the US! Now, Thom's record label tells him he is allowed to make longer music as he has proven himself as a talented musician. Now, Thom has 264 seconds to make his next single. What is the optimal bundle with this increase in song length? 3. Thom's band makes a successful album, but Thom is left scratching his head. He doesn't actually like the music all that much. Perhaps Thom did not have the correct utility function in his head. After making more music, Thom thinks his real utility function might be U(p,c)=5pkc3. Now, how should Thom construct, his new single "Karma Police" in terms of an optimal bundle? 4. "Karma Police", along with the accompanying album, come ont even better than "Creep" and Thom is much happier with the music. However, it has become harder and harder for Thom to write elements of musie the public would consider pleasing. Therefore, if Thom writes one element of publicly enjoyed music (p), he is so tired that it takes away 4 seconds from the total allotted time instesd of just the original 1. Therefore, we ean now think of Thom's budget constraint is 2644p+%. What is Thom's optimal bundle now? 5. From the last two problems, derive Thom's demand curve for p, pablicly ryjoyed elements of musie (hint: p is Q0 in this case, and price is the eflort in terms of seconds). Astume a linear dematad carve. 1. Thom is a singer-songwriter from Oxford, England who is in some band. Thom likes two things: appealing to the public, and satisfying his own creative endeavors. Therefore, every song. Thom writes has public elements (p), and creative elements (c). In fact, Thom thinks he can measure his happiness by using the utility function U(p,c)=3p2c11. However, Thom's label says he only has 236 seconds of time to make the best song he can. Each second in the song can be either "for the public" ( p ) or "for Thom" (c). How should Thom construct his debut single "Creep" in terms of the optimal bundle of public elements and creative elements? 2. "Creep" is released on September 21st, 1992 and it peaks at number 34 on the Billboard Hot 100 in the US! Now, Thom's record label tells him he is allowed to make longer music as he has proven himself as a talented musician. Now, Thom has 264 seconds to make his next single. What is the optimal bundle with this increase in song length? 3. Thom's band makes a successful album, but Thom is left scratching his head. He doesn't actually like the music all that much. Perhaps Thom did not have the correct utility function in his head. After making more music, Thom thinks his real utility function might be U(p,c)=5pkc3. Now, how should Thom construct, his new single "Karma Police" in terms of an optimal bundle? 4. "Karma Police", along with the accompanying album, come ont even better than "Creep" and Thom is much happier with the music. However, it has become harder and harder for Thom to write elements of musie the public would consider pleasing. Therefore, if Thom writes one element of publicly enjoyed music (p), he is so tired that it takes away 4 seconds from the total allotted time instesd of just the original 1. Therefore, we ean now think of Thom's budget constraint is 2644p+%. What is Thom's optimal bundle now? 5. From the last two problems, derive Thom's demand curve for p, pablicly ryjoyed elements of musie (hint: p is Q0 in this case, and price is the eflort in terms of seconds). Astume a linear dematad carve