The CEO of a furniture factory finds that the cost to manufacture beds is given by the function C(x) = 4x2 + 24x + 12, where x is the number of beds, and that the revenue for selling x beds is given by the function R(x) = 6x2 + 35x, in thousands of dollars.

a) Use the cost and revenue expressions to find the profit function, in thousands of dollars, in terms of x.

b) Find the interval for the number of beds manufactured and sold where the factory will have a positive profit.

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