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The City of Ann Arbor opened a new dog park. If D equals the number of dogs that are at the park, then happiness per dog at the park equals 40 – D. This holds so long as there are more than 10 dogs. If there are 10 dogs or fewer in the park, happiness per dog at the park equals 8. Any dogs not at the park have a happiness of 6 in all scenarios. Assume there are 100 dogs in Ann Arbor. If there are 18 dogs at the park, what is total happiness of the dogs in Ann Arbor?
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Consider the demand equation q=20,000 p^(-1.4). If the cost of production is constant at $0.50 per unit then what is the optimal price to maximize profit?
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