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A local inventor has developed a new camera technology that uses special tubes to improve the quality of the pictures it takes. To produce, each camera will cost $1,000 of fixed costs, $25 for every tube used, and $400 divided by the number of tubes used in each camera. The camera sells for $2,025.
a) Write the function P(x) for the profit on a camera, where x represents the number of tubes used in each camera.
b) What obvious restriction must be placed on x?
c) Use the function in a) to determine the number of tubes that will maximize profit.
d) Show that P(x) is maximized at the stationery point.
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