MATH 60

An inferior product with large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. If the weekly sales are given by S = 200t/(t + 1)2 where S is in millions of pesos and t in weeks. After how many weeks will the sales be maximized?

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• 2

• 3

• 4

In the coming presidential election of 1998, it is estimated that the proportions P of votes that recognizes a certain presidentiables name t months after the campaign is given by P = [7.2t/(t2 + 16)] + 0.20. After how many months is the proportional maximized?

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• 6

A car manufacturer estimates that the cost of production of x cars of a certain model is C = 20x – 0.01x2 – 800. How many cars should be produced for a minimum cost?

• a. 900

• b. 1000

• c. 1100

• d. 1200

Analysis of daily output of a factory shows that the hourly number of units y produced after t hours of production is y = 70t + (t2)/2 – t3. After how many hours will the hourly number of units be maximized and what would be the maximum hourly output?

• a. 3 hrs, 223.6

• b. 4 hrs, 273.6

• c. 5 hrs, 237.5

• d. 6 hrs, 243.5

A time study showed that on average, the productivity of a worker after t hours on the job can be modeled by the expression P = 27 + 6t – t3 where P is the number of units produced per hour. What is the maximum productivity expected?

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• 40

• 44

A viaduct is traversed by a truck running at 15 mph at the same time that another truck traveling at a speed of 30mph on the street 22ft below and at right angle to the viaduct, approached the point directly below the viaduct from a distance of 55 ft. Find the nearest distance between the trucks.

• a. 29 ft

• b. 33 ft

• c. 39 ft

• d. 44 ft

A sector is cut out of a circular disk of radius √3 and the remaining part of the disk I bent up so that the two edges join and a cone is formed. What is the largest volume for the cone?

• a. 2π/3

• b. π/3

• c. 3π/4

• d. π/4

Four squares are cut out of a rectangular cardboard 50 cm by 80 cm. in dimension and the remaining piece is folded into a closed, rectangular box with two extra flaps trucked in. What is the largest possible volume for such a box?

• a. 6000

• b. 7000

• c. 8000

• d. 9000

An isosceles triangle with equal sides of 20 cm has these sides at a variable equal angle with the base. Determine the max area of the triangle.

• a. 200 sq cm

• b. 250 sq cm

• c. 300 sq cm

• d. 280 sq cm

Formerly, for a package to go by parcel post, the sum of its length and girth could not exceed 120 cm. Find the dimensions of the rectangular package of greatest volume that could be sent.

• a. 20 x 40 x 10

• b. 20 x 20 x 20

• c. 40 x 20 x 30

• d. 20 x 20 x 40