Work these problem. (See Example.)The manager of a restaurant found that the cost of produ...

Work these problem. (See Example.)

The manager of a restaurant found that the cost of producing 100 cups of coffee is $11.02, while the cost of producing 400 cups is $40.12. Assume that the cost C (x) is a linear function of x, the number of cups produced.

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

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(b) Find the total cost of producing 1000 cups.

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(c) Find the total cost of producing 1001 cups.

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(d) Find the marginal cost of producing the 1000th cup.

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(e) What is the marginal cost of producing any cup?

Example

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