# Integration

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BPA 12203 MATHEMATICS FOR MANAGEMENT
Chapter 9

INTEGRATION

Mathematics for Management:

Integration

Application
Example 1 If the marginal proﬁt for producing x units per day is given by P (x) = 100 − 0.02x P (0) = 0

where P (x) is the proﬁt in dollars, ﬁnd the proﬁt function P and the proﬁt on 10 units of production per day.

Mathematics for Management:

Integration

Example 2 A company manufactures x HDTVs per month. The monthly marginal proﬁt (in dollars) is given by P (x) = 165 − 0.1x 0 ≤ x ≤ 4, 000

The company is currently manufacturing 1,500 HDTVs per month, but is planning to increase production. Find the change in the monthly proﬁt if monthly production is increased to 1,600 HDTVs.

Mathematics for Management:

Integration

Example 3 The market research department of a supermarket chain has determined that, for one store, the marginal price p (x) at x tubes per week for a certain brand of toothpaste is given by p (x) = −0.015e−0.01x Find the price-demand equation if the weekly demand is 50 tubes when the price of a tube is \$4.35. Find the weekly demand when the price of a tube is \$3.89.

Mathematics for Management:

Integration

Example 4 An average student enrolled in a typing class progressed at a rate of N (t) = 7e−0.1t words per minutes t weeks after enrolling in a 15-week course. a) If a student could type 25 words per minute at the beginning of the course, how many words per minute N (t) would the student be expected to type t weeks into the course? b) After completing the course?

Mathematics for Management:

Integration

Example 5 An amusement company maintains records for each video game installed in an arcade. Suppose that C(t) and R(t) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed. Suppose also that C (t)...

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