Work these problem. (See Example.)In deciding whether to set up a new manufacturing plant,...

Work these problem. (See Example.)

In deciding whether to set up a new manufacturing plant, company analysts have determined that a linear function is a reasonable estimation for the total cost C (x) in dollars of producing x items. They estimate the cost of producing 10,000 items as $547,500 and the cost of producing 50,000 items as $737,500.

(a) Find a formula for C (x).

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(b) Find the total cost of producing 100,000 items.

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(c) Find the marginal cost of the items to be produced in this plant.

Example

An electronics company manufactures handheld PCs. The cost function for one of its models is C(x) = 160x + 750,000.