To earn extra money, you and your friends decide to start a carwash. Based on some...

  

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To earn extra money, you and your friends decide to start a carwash. Based on some data you have collected, you predict that when you charge p dollar to wash and detail a car, you will have a demand of D cars each day, given by the model D(p) = 0.01(32-0.8p)³. Each time you clean a customer's car, there are some costs to you, the carwash owners. Water, soap, electricity, sponges, vacuum cleaners, and other materials all factor into the associated costs. To wash a total of D cars in one day, you would have to pay C(D)= 0.015D² + 1.25D + 890 dollars. Given this information, answer the following: a. Use the elasticity of demand to compute the unit price that maximizes revenue. b. What is the demand at the above price? Round and label appropriately. c. Use the "Marginal Analysis Criterion for Minimum Average Cost" to find the number of cars that need to be serviced to minimize average cost. d. What is the unit price that should be changed to minimize average cost? e. Suppose you must choose between the two above unit prices. Which should you choose, and why? Hint: Which situation would bring in more money each day? To earn extra money, you and your friends decide to start a carwash. Based on some data you have collected, you predict that when you charge p dollar to wash and detail a car, you will have a demand of D cars each day, given by the model D(p) = 0.01(32-0.8p)³. Each time you clean a customer's car, there are some costs to you, the carwash owners. Water, soap, electricity, sponges, vacuum cleaners, and other materials all factor into the associated costs. To wash a total of D cars in one day, you would have to pay C(D)= 0.015D² + 1.25D + 890 dollars. Given this information, answer the following: a. Use the elasticity of demand to compute the unit price that maximizes revenue. b. What is the demand at the above price? Round and label appropriately. c. Use the "Marginal Analysis Criterion for Minimum Average Cost" to find the number of cars that need to be serviced to minimize average cost. d. What is the unit price that should be changed to minimize average cost? e. Suppose you must choose between the two above unit prices. Which should you choose, and why? Hint: Which situation would bring in more money each day?