Download Minima and Maxima: Number Problems

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Minima and Maxima: Number Problems
MPM2D
1.
Find two numbers whose sum is 36 and whose product is a maximum. [18, 18]
2.
The sum of a positive integer plus twice a second positive integer is 16. Find
the integers that yield a maximum product. [4, 8]
3.
Find two nonnegative numbers whose sum is 12 and the sum of their squares
is a minimum. [6, 6]
4.
The difference of two numbers is 100. Find two such numbers so that their
product is a minimum. [-50, 50]
5.
Find two numbers which have a difference of 7 and a product that is a
7 7
minimum.
,
2 2
6.
Find two numbers whose difference is 13 and whose squares when added
13 13 169
together yield a minimum. What is the minimum value?
,
,
2
2 2
7.
Two numbers are related in the manner 3x +y = 42. Find the values of x and
y so that their product is a maximum. What is the product? [7, 21, 147]
8.
What are the values of two positive numbers whose sum is 60 and whose
product yields a maximum. [30, 30]
9.
Two numbers are related by the equation 4x + y = 64. Find the values of the
numbers so that their product is a maximum. What is the product?
[8, 32, 256]
10.
Two numbers are given by m and m-3. Find the numbers if the sum of their
3 3
,
squares is a minimum.
2 2
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