Download More Word Problem Practice Name: ______ Pre

More Word Problem Practice
Pre-Calc. for AP Prep.
1)
Name: ___________
Date: ___________
Find the whole number values of x and y that minimize C = 6x + 9y.
 x  2 y  50

 2 x  y  60
 x  0, y  0

2)
Baking a tray of corn muffins takes 4 cups milk and 3 cups wheat flour. A tray of bran
muffins takes 2 cups milk and 3 cups wheat flour. A baker has 16 cups of milk and 15
cups wheat flour. He makes $3 profit per tray of corn muffins and $2 profit per tray of
bran muffins. How many trays of each type of muffin should the baker make to
maximize his profit?
3)
A biologist is developing two new strains of bacteria. Each sample of Type I
bacteria produces four new viable bacteria and each sample of Type II produces
three new viable bacteria. Altogether, at least 240 new viable bacteria must be
produced. At least 30, but not more than 60, of the original samples must be Type
I. No more than 70 of the samples can be Type II. A sample of Type I costs $5
and a sample of Type II costs $7. How many samples of Type II bacteria should
be used to minimize cost?
4)
Teams chosen from 30 forest rangers and 16 trainees are planting trees. An
experienced team consisting of two rangers can plant 500 trees per week. A
training team of one ranger and two trainees can plant 200 trees per week. How
many of each type of team should be formed to maximize the number of trees
planted?
5)
A cologne bottle is to be made in the shape of a cylinder with a hemispherical top. The
cost to make the cylindrical portion of the bottle is 8 cents per square inch while the cost
to make the hemispherical portion of the bottle is 5 cents per square inch. If the base of
the bottle must be twice the radius, write an expression to represent the cost of producing
the bottle.
6)
In 1978, a ruling by the Civil Aeronautics Board allowed Federal Express to purchase
larger aircraft. Federal Express’s options included 20 Boeing 727s that United Airlines
was retiring and/or the French-built Dassault Fanjet Falcon 20. To aid in their decision,
executives at Federal Express found that the direct operating cost of a Boeing 727 was
$1400 per hour and for a Falcon 20 was $500 per hour. Additionaly, they found that the
payload of a Boeing 727 is 42,000 pounds and of a Falcon 20 is 6000 pounds. Federal
Express is faced with the following constraints:
 Hourly operating cost was limited to $35,000
 Total payload had to be at least 672,000 pounds
 Only twenty 727s were available.
Given the constraints, how many of each kind of aircraft should Federal Express have
purchased to maximize the number of aircraft?
7)
The perimeter of a rectangle is 50 feet. Describe the possible lengths of a side if the area
of the rectangle is not to exceed 114 square feet.
8)
9)
Keng creates a painting on a rectangular canvas with a width that is four inches longer
than the height.
a)
Write a polynomial expression, in simplified form, that represents the area of the
canvas.
b)
Keng adds a 3-inch wide frame around all sides of his canvas. Write a
polynomial expression, in simplified form, that represents the total area of the
canvas and the frame.
c)
Keng is unhappy with his 3-inch wide frame, so he decides to put a frame with a
different width around his canvas. The total area of the canvas and the new frame
is given by h2 + 8h + 12 where h is the height of the canvas. Determine the width
of the new frame. Explain why you did each step.