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Question: i only wanna the answer for the question d please...

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(1) When Jake works from home, he typically spends 40 minutes of each hour on research, and 10 on teaching, and drinks half a cup of coffee. (The remaining time is spent on the internet.) For each hour he works in the math department, he spends around 20 minutes on research and 30 on teaching, and doesnt drink any coffee. Lastly, if he works at a coffeeshop for an hour, he spends 25 minutes each on research and teaching, and drinks a cup of coffee. Note: be careful about units of minutes versus hours (a) Last week, Jake spent 10 hours working from home, 15 hours working in his office in Padelford Hall, and 2 hours working at Cafe Allegro. Compute what was accomplished, and express the result as a vector equation b) This week. Jake has 15 hours of research to work on and 10 hours of work related to teaching. He also wants 11 cups of coffee, because... of... very important reasons. How much time should he spend working from home, from his office, and from the coffeeshop? (c) Describe the situation in part (b) as a vector equation and a matrix equation At-. What do the vectors t and w mean in this context? For which other vectors w does the equation At - w have a solution? (d) Jake tries working in the math department lounge for an hour, and gets 30 minutes of research and 20 minutes of teaching work done, while having time to drink 1 of a cup of coffee. Not bad. But Jakes colleague Vasu claims that theres no need to work in the lounge - the other options already give enough flexibility. Is he right? Explain mathematically 3I only wanna the answer for the question (d). please explain how it will be related to flexibility and what definition it connects to. Thank you.

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