Pearl Ltd. intends to manufacture and market mechanical weighing scales. Their research department has derived the price-demand equation and the cost function, respectively as x = 6200 - 50p and C(x) = 7400 + 70x where x is the number of scales that can be sold at Sp per unit and C(x) represents the total cost of producing x scales. (a) Express the price p as a function of the demand x. Find the domain of this function. (b) Find the exact cost of producing the 45th scale.

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