Math 71 Supplement 10-23-09

# Math 71 Supplement - Math 71 Supplement Suppose x units of a product is produced in some interval \$C x is the cost of producing x units and \$R x is

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Math 71 Supplement 10-23-09 Suppose x units of a product is produced in some interval, \$ C x ( ) is the cost of producing x units, and \$ R x ( ) is the revenue of producing x units. Then the profit \$ P x ( ) is given by P x ( ) = R x ( ) " C x ( ) . The derivatives of these functions C ' x ( ) , R ' x ( ) , P ' x ( ) are called marginal cost , marginal revenue , and marginal profit , respectively. They represent the rates of changes. However, the practical way to think about these are the following: C ' x ( ) " C x + 1 ( ) # C x ( ) , the cost of producing one product when x units are produced. R ' x ( ) " R x + 1 ( ) # R x ( ) , the revenue earned from one product when x units are produced. P ' x ( ) " P x + 1 ( ) # P x ( ) , the profit from selling one product when x units are produced. Example: A company is planning to manufacture and market a microwave oven. After extensive market analysis, the development and market department provides the following results: a weekly demand of 200 microwave oven at \$160 per unit, and a weekly demand of 300 microwave oven at \$140 per unit. The weekly fixed cost of

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## This note was uploaded on 09/08/2010 for the course MATH 71 at San Jose State University .

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Math 71 Supplement - Math 71 Supplement Suppose x units of a product is produced in some interval \$C x is the cost of producing x units and \$R x is

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