Dr. Katiraie
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Summer 08
Quiz 3
MA160
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Solve the problem.
1) If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where
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p(x) == 61 -
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Find the number of units that must be produced and sold in order to yield the maximum profit, given the
following equations for revenue and cost:
R(x) == 40x - 0.5x 2
C(x) = 8x + 5.
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(lff+.s \ 3) A rectangular field is to be enclosed on four sides with a fence. Fencing costs $3 per foot for two opposite sides,
C Y and $2 per foot for the other two sides. Find the dimensions of the field of area 850 ft2 that would be the
cheapest to enclose.
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4) A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages
40,000 people per game. For every increase of $1, it loses 5,000 people. What price per ticket should be charged
in order to maximize revenue?
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5) A carpenter is building a rectangular room with afixed perimeter of 440 ft. What are the dimensions of the
largest room that can be built? What is its area?
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6) A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 53 «:3.
What dimensions yield the mirumum surfacearea? Round to the nearest tenth, if necessary.
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"oi:Katiraie
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Summer 08
Quiz 3
MA160
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Solve the problem.
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1) If the price charged for a candy Mr is p(x) cents, then x thousand candy Mrs will be sold in a certain city, where
P (x) = 125 - ~. How many candy Mrs must be sold to maximize revenue?
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2) Find the number of units that must be produced and sold in order to yield the maximum profit, given the
following equations for revenue and cost
R(x) = SOx - 0.5x 2
C(x) =9x + 6.
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3) A rectangular field is to be enclosed on four sides with a fence. Fencing costs $6 per foot for two opposite sides,
and $3 per foot for the other two sides. Find the dimensions of the field of area 690 ft2 that would be the
cheapest to enclose.
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4) A baseball team is trying to determine what price to charge for tickets. At a price of $10 per ticket, it averages
45,000 people per game. For every increase of $1, it loses 5,000 people. What price per ticket should be charged
in order to maximize revenue?
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5) A carpenter is building a rectangular room with a fixed perimeter of 100 ft What are the dimensions of the
largest room that can be built? What is its area?
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6) A company is constructing an~square-based,rectangular metal tank that will ha~~a'~~cl56 '. it3.
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