5. A recent study estimated that the average cost per patient per year in U.S. nursing homes is described by the equation: $C = 70 - .22X + .002X^2$ where $X$ is the number of patients in a given nursing home on average over a year. A. How big should a nursing home be (in average number of patients over a year) if the goal is to minimize the average cost per patient? B. Show that your result minimizes rather than maximizes average cost per patient.
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