5. The annual output for a luxury hotel chain is given by Q = 30K2/5 L1/2 R1/4, where K, L and R are the capital, labor and real estate inputs, all measured in $1,000,000 s, and Q is the average number of rooms rented per day. The hotel chain's annual budget is B = $69 million. (a) How should they allocate this budget to the three inputs in order to maximize their annual output? What is the maximum output? (b) What is the approximate change in the firm's maximum output if their annual budget increases by $500,000? Explain your answer.

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Chapter1: Making Economics Decisions
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5. The annual output for a luxury hotel chain is given by Q = 30K²/5 L¹/2 R¹/4, where K, L and R
are the capital, labor and real estate inputs, all measured in $1,000,000 s, and Q is the average
number of rooms rented per day.
The hotel chain's annual budget is B = $69 million.
(a) How should they allocate this budget to the three inputs in order to maximize their
annual output? What is the maximum output?
(b) What is the approximate change in the firm's maximum output if their annual budget
increases by $500,000? Explain your answer.
Transcribed Image Text:5. The annual output for a luxury hotel chain is given by Q = 30K²/5 L¹/2 R¹/4, where K, L and R are the capital, labor and real estate inputs, all measured in $1,000,000 s, and Q is the average number of rooms rented per day. The hotel chain's annual budget is B = $69 million. (a) How should they allocate this budget to the three inputs in order to maximize their annual output? What is the maximum output? (b) What is the approximate change in the firm's maximum output if their annual budget increases by $500,000? Explain your answer.
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